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Ζ(3)는 무리수이다(아페리의 정리) - 편집 역사
2024-03-29T15:17:18Z
이 문서의 편집 역사
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2021년 2월 17일 (수) 11:55에 Pythagoras0님의 편집
2021-02-17T11:55:20Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2021년 2월 17일 (수) 11:55 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l275" >275번째 줄:</td>
<td colspan="2" class="diff-lineno">275번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* F. M. S. Lima, Beukers-like proofs of irrationality for <math>ζ{(2)}</math> and <math>ζ{(3)}</math>, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* F. M. S. Lima, Beukers-like proofs of irrationality for <math>ζ{(2)}</math> and <math>ζ{(3)}</math>, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== 메타데이터 ==</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>==메타데이터==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===위키데이터===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===위키데이터===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* ID : [https://www.wikidata.org/wiki/Q965545 Q965545]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* ID : [https://www.wikidata.org/wiki/Q965545 Q965545]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Spacy 패턴 목록===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [{'LOWER': 'roger'}, {'LEMMA': 'Apéry'}]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [{'LOWER': 'roger'}, {'LEMMA': 'Apery'}]</ins></div></td></tr>
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Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=49152&oldid=prev
Pythagoras0: /* 메타데이터 */ 새 문단
2020-12-28T14:40:22Z
<p><span dir="auto"><span class="autocomment">메타데이터: </span> 새 문단</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2020년 12월 28일 (월) 14:40 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l274" >274번째 줄:</td>
<td colspan="2" class="diff-lineno">274번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* F. M. S. Lima, Beukers-like proofs of irrationality for <math>ζ{(2)}</math> and <math>ζ{(3)}</math>, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* F. M. S. Lima, Beukers-like proofs of irrationality for <math>ζ{(2)}</math> and <math>ζ{(3)}</math>, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== 메타데이터 ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===위키데이터===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* ID : [https://www.wikidata.org/wiki/Q965545 Q965545]</ins></div></td></tr>
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Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=41254&oldid=prev
2020년 11월 13일 (금) 17:13에 Pythagoras0님의 편집
2020-11-13T17:13:20Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2020년 11월 13일 (금) 17:13 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9" >9번째 줄:</td>
<td colspan="2" class="diff-lineno">9번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 1979년 아페리 (Apéry)는 <math>\zeta(3)</math> 이 무리수임을 보였으며, 이후로 <math>\zeta(3)</math> 는 [[아페리 상수]]라 불린다.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 1979년 아페리 (Apéry)는 <math>\zeta(3)</math> 이 무리수임을 보였으며, 이후로 <math>\zeta(3)</math> 는 [[아페리 상수]]라 불린다.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 아페리의 아이디어에 대해서는 [[아페리(Apéry) 점화식]] 항목 참조</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 아페리의 아이디어에 대해서는 [[아페리(Apéry) 점화식]] 항목 참조</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del class="diffchange diffchange-inline">$</del>\zeta(3)/\pi^3<del class="diffchange diffchange-inline">$</del>가 유리수인지 무리수인지를 보이는 것은 아페리 상수에 대한 주요 미해결 문제</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins class="diffchange diffchange-inline"><math></ins>\zeta(3)/\pi^3<ins class="diffchange diffchange-inline"></math></ins>가 유리수인지 무리수인지를 보이는 것은 아페리 상수에 대한 주요 미해결 문제</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19" >19번째 줄:</td>
<td colspan="2" class="diff-lineno">19번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===증명의 아이디어===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===증명의 아이디어===</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>다음 조건을 만족하는 정수열 <math>p_n,q_n>0</math>과 상수 <del class="diffchange diffchange-inline">$</del>\delta>0<del class="diffchange diffchange-inline">$</del>가 존재함을 보일 수 있다</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>다음 조건을 만족하는 정수열 <math>p_n,q_n>0</math>과 상수 <ins class="diffchange diffchange-inline"><math></ins>\delta>0<ins class="diffchange diffchange-inline"></math></ins>가 존재함을 보일 수 있다</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">$$</del>|\zeta(3)-\frac{p_n}{q_n}|<\frac{1}{q_n^{1+\delta}},\quad n=1,2,\cdots<del class="diffchange diffchange-inline">$$</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:<math></ins>|\zeta(3)-\frac{p_n}{q_n}|<\frac{1}{q_n^{1+\delta}},\quad n=1,2,\cdots<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>이로부터 [[무리수와 디오판투스 근사]]의 아이디어를 적용하여, <del class="diffchange diffchange-inline">$</del>\zeta(3)<del class="diffchange diffchange-inline">$</del>가 무리수임을 증명한다</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>이로부터 [[무리수와 디오판투스 근사]]의 아이디어를 적용하여, <ins class="diffchange diffchange-inline"><math></ins>\zeta(3)<ins class="diffchange diffchange-inline"></math></ins>가 무리수임을 증명한다</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===보조정리 1===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===보조정리 1===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>충분히 큰 n에 대하여, <del class="diffchange diffchange-inline">$</del>1, 2, 3, \cdots, n<del class="diffchange diffchange-inline">$ </del>의 최소공배수(<math>d_n</math>라 쓰자)는 <math>2.99^n</math> 보다 작다.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>충분히 큰 n에 대하여, <ins class="diffchange diffchange-inline"><math></ins>1, 2, 3, \cdots, n<ins class="diffchange diffchange-inline"></math> </ins>의 최소공배수(<math>d_n</math>라 쓰자)는 <math>2.99^n</math> 보다 작다.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>([[1부터 n까지의 최소공배수]] 항목 참조)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>([[1부터 n까지의 최소공배수]] 항목 참조)</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l64" >64번째 줄:</td>
<td colspan="2" class="diff-lineno">64번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>이를 이용하여 다음을 얻는다 :</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>이를 이용하여 다음을 얻는다 :</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">$</del>r=s<del class="diffchange diffchange-inline">$ </del>일 때,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><math></ins>r=s<ins class="diffchange diffchange-inline"></math> </ins>일 때,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{x^{r+\delta} y^{s+\delta}}{1-xy}dxdy =\sum_{k=0}^{\infty} \frac{1}{(1+k+r+\delta )^2}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{x^{r+\delta} y^{s+\delta}}{1-xy}dxdy =\sum_{k=0}^{\infty} \frac{1}{(1+k+r+\delta )^2}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">$</del>r>s<del class="diffchange diffchange-inline">$ </del>일 때,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><math></ins>r>s<ins class="diffchange diffchange-inline"></math> </ins>일 때,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{x^{r+\delta} y^{s+\delta}}{1-xy}dxdy =\frac{1}{r-s}\left(\frac{1}{s+1+\delta}+\cdots +\frac{1}{r+\delta} \right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{x^{r+\delta} y^{s+\delta}}{1-xy}dxdy =\frac{1}{r-s}\left(\frac{1}{s+1+\delta}+\cdots +\frac{1}{r+\delta} \right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l75" >75번째 줄:</td>
<td colspan="2" class="diff-lineno">75번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>위 식의 양변을 <math>\delta</math>로 미분하면,</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>위 식의 양변을 <math>\delta</math>로 미분하면,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">$</del>r=s<del class="diffchange diffchange-inline">$</del>일 때,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><math></ins>r=s<ins class="diffchange diffchange-inline"></math></ins>일 때,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{-x^{\delta +r} y^{\delta +s} \log (xy)}{1-xy}dxdy=\sum_{k=0}^{\infty}\frac{2}{(1+k+r+\delta )^3}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{-x^{\delta +r} y^{\delta +s} \log (xy)}{1-xy}dxdy=\sum_{k=0}^{\infty}\frac{2}{(1+k+r+\delta )^3}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">$</del>r>s<del class="diffchange diffchange-inline">$</del>일 때,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><math></ins>r>s<ins class="diffchange diffchange-inline"></math></ins>일 때,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{-x^{\delta +r} y^{\delta +s} \log (xy)}{1-xy}dxdy=\frac{1}{r-s}\left(\frac{1}{(s+1+\delta)^2}+\cdots +\frac{1}{(r+\delta)^2} \right)</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_{0}^{1}\int_{0}^{1}\frac{-x^{\delta +r} y^{\delta +s} \log (xy)}{1-xy}dxdy=\frac{1}{r-s}\left(\frac{1}{(s+1+\delta)^2}+\cdots +\frac{1}{(r+\delta)^2} \right)</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>■ </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>■ </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l255" >255번째 줄:</td>
<td colspan="2" class="diff-lineno">255번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Zudilin, W. W. 2001. “One of the Numbers Ζ(5), Ζ(7), Ζ(9), Ζ(11) Is Irrational.” Russian Mathematical Surveys 56 (4) (August 31): 774. doi:10.1070/RM2001v056n04ABEH000427.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Zudilin, W. W. 2001. “One of the Numbers Ζ(5), Ζ(7), Ζ(9), Ζ(11) Is Irrational.” Russian Mathematical Surveys 56 (4) (August 31): 774. doi:10.1070/RM2001v056n04ABEH000427.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [http://arxiv.org/abs/math/0201024 An Apéry-like difference equation for Catalan's constant] Wadim Zudilin, 2002</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [http://arxiv.org/abs/math/0201024 An Apéry-like difference equation for Catalan's constant] Wadim Zudilin, 2002</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* '''[Huylebrouck2001]'''[http://mathdl.maa.org/mathDL/?pa=content&sa=viewDocument&nodeId=2886 Similarities in Irrationality Proofs for <del class="diffchange diffchange-inline">$</del>\pi<del class="diffchange diffchange-inline">$</del>, <del class="diffchange diffchange-inline">$</del>\ln 2<del class="diffchange diffchange-inline">$</del>, <del class="diffchange diffchange-inline">$</del>\zeta(2)<del class="diffchange diffchange-inline">$ </del>and <del class="diffchange diffchange-inline">$</del>\zeta(3)<del class="diffchange diffchange-inline">$</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* '''[Huylebrouck2001]'''[http://mathdl.maa.org/mathDL/?pa=content&sa=viewDocument&nodeId=2886 Similarities in Irrationality Proofs for <ins class="diffchange diffchange-inline"><math></ins>\pi<ins class="diffchange diffchange-inline"></math></ins>, <ins class="diffchange diffchange-inline"><math></ins>\ln 2<ins class="diffchange diffchange-inline"></math></ins>, <ins class="diffchange diffchange-inline"><math></ins>\zeta(2)<ins class="diffchange diffchange-inline"></math> </ins>and <ins class="diffchange diffchange-inline"><math></ins>\zeta(3)<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Dirk Huylebrouck, The American Mathematical Monthly,Vol. 108, March 2001 pp. 222-231</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Dirk Huylebrouck, The American Mathematical Monthly,Vol. 108, March 2001 pp. 222-231</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Beukers, F. 1987. “Irrationality Proofs Using Modular Forms.” Astérisque (147-148): 271–283, 345.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Beukers, F. 1987. “Irrationality Proofs Using Modular Forms.” Astérisque (147-148): 271–283, 345.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* '''[Beukers1979]'''[http://dx.doi.org/10.1112%2Fblms%2F11.3.268 A note on the irrationality of <del class="diffchange diffchange-inline">$</del>\zeta(2)<del class="diffchange diffchange-inline">$ </del>and <del class="diffchange diffchange-inline">$</del>\zeta(3)<del class="diffchange diffchange-inline">$</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* '''[Beukers1979]'''[http://dx.doi.org/10.1112%2Fblms%2F11.3.268 A note on the irrationality of <ins class="diffchange diffchange-inline"><math></ins>\zeta(2)<ins class="diffchange diffchange-inline"></math> </ins>and <ins class="diffchange diffchange-inline"><math></ins>\zeta(3)<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** F. Beukers (1979). Bull. London Math. Soc. 11: 268\[Dash]272.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** F. Beukers (1979). Bull. London Math. Soc. 11: 268\[Dash]272.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* A. van der Poorten [http://dx.doi.org/10.1007/FBF03028234 A proof that Euler missed ... Apéry's Proof of the irrationality of <del class="diffchange diffchange-inline">$</del>\zeta(3)<del class="diffchange diffchange-inline">$</del>], The Mathematical Intelligencer 1 (4): 195-203, 1979</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* A. van der Poorten [http://dx.doi.org/10.1007/FBF03028234 A proof that Euler missed ... Apéry's Proof of the irrationality of <ins class="diffchange diffchange-inline"><math></ins>\zeta(3)<ins class="diffchange diffchange-inline"></math></ins>], The Mathematical Intelligencer 1 (4): 195-203, 1979</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** http://jones.math.unibas.ch/~massierer/algebra-hs11/vanderPoorten2.pdf</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** http://jones.math.unibas.ch/~massierer/algebra-hs11/vanderPoorten2.pdf</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l273" >273번째 줄:</td>
<td colspan="2" class="diff-lineno">273번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== 리뷰, 에세이, 강의노트 ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== 리뷰, 에세이, 강의노트 ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* F. M. S. Lima, Beukers-like proofs of irrationality for <del class="diffchange diffchange-inline">$</del>ζ{(2)}<del class="diffchange diffchange-inline">$ </del>and <del class="diffchange diffchange-inline">$</del>ζ{(3)}<del class="diffchange diffchange-inline">$</del>, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* F. M. S. Lima, Beukers-like proofs of irrationality for <ins class="diffchange diffchange-inline"><math></ins>ζ{(2)}<ins class="diffchange diffchange-inline"></math> </ins>and <ins class="diffchange diffchange-inline"><math></ins>ζ{(3)}<ins class="diffchange diffchange-inline"></math></ins>, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=32752&oldid=prev
Pythagoras0: section '리뷰, 에세이, 강의노트' added
2016-05-18T08:22:56Z
<p>section '리뷰, 에세이, 강의노트' added</p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2016년 5월 18일 (수) 08:22 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l270" >270번째 줄:</td>
<td colspan="2" class="diff-lineno">270번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:무리수와 초월수]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:무리수와 초월수]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:적분]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:적분]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== 리뷰, 에세이, 강의노트 ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* F. M. S. Lima, Beukers-like proofs of irrationality for $ζ{(2)}$ and $ζ{(3)}$, arXiv:1308.2720 [math.NT], August 12 2013, http://arxiv.org/abs/1308.2720</ins></div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=31213&oldid=prev
Pythagoras0: /* 관련도서 */
2015-03-22T02:28:26Z
<p><span dir="auto"><span class="autocomment">관련도서</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2015년 3월 22일 (일) 02:28 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l269" >269번째 줄:</td>
<td colspan="2" class="diff-lineno">269번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:상수]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:상수]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:무리수와 초월수]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[분류:무리수와 초월수]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[분류:적분]]</ins></div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=31212&oldid=prev
Pythagoras0: /* 보조정리 4 */
2015-03-22T02:26:48Z
<p><span dir="auto"><span class="autocomment">보조정리 4</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="ko">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2015년 3월 22일 (일) 02:26 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l127" >127번째 줄:</td>
<td colspan="2" class="diff-lineno">127번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>Q(x)=x^n(1-x)^n</math> 라 두자.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>Q(x)=x^n(1-x)^n</math> 라 두자.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>0\leq k < n</math> 일 때 <math>Q^{(k)}(0)=Q^{(k)}(1)=0</math>이므로. <del class="diffchange diffchange-inline">부분적분을 </del>반복적용하면,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>0\leq k < n</math> 일 때 <math>Q^{(k)}(0)=Q^{(k)}(1)=0</math>이므로. <ins class="diffchange diffchange-inline">[[부분적분]]을 </ins>반복적용하면,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_0^1Q^{(n)}(x)f (x)\,dx=-\int_0^1Q^{(n-1)}(x)f'(x)\,dx=\cdots=(-1)^n \int_0^1 Q(x)f^{(n)}(x)\,dx</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>\int_0^1Q^{(n)}(x)f (x)\,dx=-\int_0^1Q^{(n-1)}(x)f'(x)\,dx=\cdots=(-1)^n \int_0^1 Q(x)f^{(n)}(x)\,dx</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>P_n(x) = \frac{Q^{(n)}(x)}{n!}</math> 이므로 증명되었다. ■</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>P_n(x) = \frac{Q^{(n)}(x)}{n!}</math> 이므로 증명되었다. ■</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l138" >138번째 줄:</td>
<td colspan="2" class="diff-lineno">138번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>I_n = \int_0^1\int_0^1\frac{-\log(xy)}{1-xy}P_n(x)P_n(y) dxdy</math> 라고 하자.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>I_n = \int_0^1\int_0^1\frac{-\log(xy)}{1-xy}P_n(x)P_n(y) dxdy</math> 라고 하자.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===보조정리 5===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===보조정리 5===</div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=31010&oldid=prev
2015년 1월 24일 (토) 11:01에 Pythagoras0님의 편집
2015-01-24T11:01:19Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2015년 1월 24일 (토) 11:01 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7" >7번째 줄:</td>
<td colspan="2" class="diff-lineno">7번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** <math>\zeta(2n+1)</math> 중 무리수인 것은 무수히 많다.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** <math>\zeta(2n+1)</math> 중 무리수인 것은 무수히 많다.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** <math>\zeta(5), \zeta(7), \zeta(9), \zeta(11)</math> 중 적어도 하나는 무리수이다.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** <math>\zeta(5), \zeta(7), \zeta(9), \zeta(11)</math> 중 적어도 하나는 무리수이다.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 1979년 <del class="diffchange diffchange-inline">Apery는 </del><math>\zeta(3)</math> 이 무리수임을 보였으며, 이후로 <math>\zeta(3)</math> 는 아페리 <del class="diffchange diffchange-inline">(Apéry) 상수라 </del>불린다.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 1979년 <ins class="diffchange diffchange-inline">아페리 (Apéry)는 </ins><math>\zeta(3)</math> 이 무리수임을 보였으며, 이후로 <math>\zeta(3)</math> 는 <ins class="diffchange diffchange-inline">[[</ins>아페리 <ins class="diffchange diffchange-inline">상수]]라 </ins>불린다.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">* 아페리의 증명에는 다음과 같은 등식이 사용되었다</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:<math>\zeta(3) = \frac{5}{2} \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^3\binom{2n}{n}}</math> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 아페리의 아이디어에 대해서는 [[아페리(Apéry) 점화식]] 항목 참조</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 아페리의 아이디어에 대해서는 [[아페리(Apéry) 점화식]] 항목 참조</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* $\zeta(3)/\pi^3$가 유리수인지 무리수인지를 보이는 것은 아페리 상수에 대한 주요 미해결 문제</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* $\zeta(3)/\pi^3$가 유리수인지 무리수인지를 보이는 것은 아페리 상수에 대한 주요 미해결 문제</div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=31004&oldid=prev
Pythagoras0: /* 관련된 항목들 */
2015-01-24T08:34:30Z
<p><span dir="auto"><span class="autocomment">관련된 항목들</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="ko">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2015년 1월 24일 (토) 08:34 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l242" >242번째 줄:</td>
<td colspan="2" class="diff-lineno">242번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[정수에서의 리만제타함수의 값]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[정수에서의 리만제타함수의 값]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[아페리(Apéry) 점화식]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[아페리(Apéry) 점화식]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [[아페리 상수]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[파이 π는 무리수이다]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[파이 π는 무리수이다]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==매스매티카 파일 및 계산 리소스==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==매스매티카 파일 및 계산 리소스==</div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=30824&oldid=prev
Pythagoras0: /* 관련논문 */
2014-12-29T08:15:41Z
<p><span dir="auto"><span class="autocomment">관련논문</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← 이전 판</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2014년 12월 29일 (월) 08:15 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l258" >258번째 줄:</td>
<td colspan="2" class="diff-lineno">258번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==관련논문==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==관련논문==</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Brown, Francis. ‘Irrationality Proofs for Zeta Values, Moduli Spaces and Dinner Parties’. arXiv:1412.6508 [math], 19 December 2014. http://arxiv.org/abs/1412.6508.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Zudilin, W. W. 2001. “One of the Numbers Ζ(5), Ζ(7), Ζ(9), Ζ(11) Is Irrational.” Russian Mathematical Surveys 56 (4) (August 31): 774. doi:10.1070/RM2001v056n04ABEH000427.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Zudilin, W. W. 2001. “One of the Numbers Ζ(5), Ζ(7), Ζ(9), Ζ(11) Is Irrational.” Russian Mathematical Surveys 56 (4) (August 31): 774. doi:10.1070/RM2001v056n04ABEH000427.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [http://arxiv.org/abs/math/0201024 An Apéry-like difference equation for Catalan's constant] Wadim Zudilin, 2002</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [http://arxiv.org/abs/math/0201024 An Apéry-like difference equation for Catalan's constant] Wadim Zudilin, 2002</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l267" >267번째 줄:</td>
<td colspan="2" class="diff-lineno">268번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* A. van der Poorten [http://dx.doi.org/10.1007/FBF03028234 A proof that Euler missed ... Apéry's Proof of the irrationality of $\zeta(3)$], The Mathematical Intelligencer 1 (4): 195-203, 1979</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* A. van der Poorten [http://dx.doi.org/10.1007/FBF03028234 A proof that Euler missed ... Apéry's Proof of the irrationality of $\zeta(3)$], The Mathematical Intelligencer 1 (4): 195-203, 1979</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** http://jones.math.unibas.ch/~massierer/algebra-hs11/vanderPoorten2.pdf</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** http://jones.math.unibas.ch/~massierer/algebra-hs11/vanderPoorten2.pdf</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==관련도서==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==관련도서==</div></td></tr>
</table>
Pythagoras0
https://wiki.mathnt.net/index.php?title=%CE%96(3)%EB%8A%94_%EB%AC%B4%EB%A6%AC%EC%88%98%EC%9D%B4%EB%8B%A4(%EC%95%84%ED%8E%98%EB%A6%AC%EC%9D%98_%EC%A0%95%EB%A6%AC)&diff=28776&oldid=prev
2013년 12월 27일 (금) 11:50에 Pythagoras0님의 편집
2013-12-27T11:50:23Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2013년 12월 27일 (금) 11:50 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l262" >262번째 줄:</td>
<td colspan="2" class="diff-lineno">262번째 줄:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''[Huylebrouck2001]'''[http://mathdl.maa.org/mathDL/?pa=content&sa=viewDocument&nodeId=2886 Similarities in Irrationality Proofs for $\pi$, $\ln 2$, $\zeta(2)$ and $\zeta(3)$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''[Huylebrouck2001]'''[http://mathdl.maa.org/mathDL/?pa=content&sa=viewDocument&nodeId=2886 Similarities in Irrationality Proofs for $\pi$, $\ln 2$, $\zeta(2)$ and $\zeta(3)$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Dirk Huylebrouck, The American Mathematical Monthly,Vol. 108, March 2001 pp. 222-231</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Dirk Huylebrouck, The American Mathematical Monthly,Vol. 108, March 2001 pp. 222-231</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Beukers, F. 1987. “Irrationality Proofs Using Modular Forms.” Astérisque (147-148): 271–283, 345.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''[Beukers1979]'''[http://dx.doi.org/10.1112%2Fblms%2F11.3.268 A note on the irrationality of $\zeta(2)$ and $\zeta(3)$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* '''[Beukers1979]'''[http://dx.doi.org/10.1112%2Fblms%2F11.3.268 A note on the irrationality of $\zeta(2)$ and $\zeta(3)$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** F. Beukers (1979). Bull. London Math. Soc. 11: 268\[Dash]272.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** F. Beukers (1979). Bull. London Math. Soc. 11: 268\[Dash]272.</div></td></tr>
</table>
Pythagoras0