로그 탄젠트 적분(log tangent integral) - 편집 역사

2020년 12월 28일 (월) 10:17에 Pythagoras0님의 편집

2020-12-28T10:17:40Z

차이 보기

2020년 11월 16일 (월) 12:00에 Pythagoras0님의 편집

2020-11-16T12:00:13Z

2014년 7월 13일 (일) 23:22에 Pythagoras0님의 편집

2014-07-13T23:22:08Z

2014년 7월 13일 (일) 23:17에 Pythagoras0님의 편집

2014-07-13T23:17:52Z

2013년 2월 11일 (월) 16:12에 Pythagoras0님의 편집

2013-02-11T16:12:28Z

2013년 1월 28일 (월) 22:14에 Pythagoras0님의 편집

2013-01-28T22:14:16Z

Pythagoras0: /* 매스매티카 파일 및 계산 리소스 */

2013-01-27T09:41:57Z

매스매티카 파일 및 계산 리소스

Pythagoras0: /* 메모 */

2013-01-27T09:40:26Z

메모

Pythagoras0: 찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

2013-01-14T22:55:37Z

찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

Pythagoras0: 찾아 바꾸기 – “
$” 문자열을 “: ” 문자열로$

2013-01-12T17:32:38Z

찾아 바꾸기 – “<br><math>” 문자열을 “:<math>” 문자열로

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
-* [[로그 사인 적분 (log sine integrals)]]과 밀접하게 관련되어 있음<br>
+* [[로그 사인 적분 (log sine integrals)]]과 밀접하게 관련되어 있음
 *  다음과 같은 정적분값의 계산:<math>\int_{\pi/4}^{\pi/2} \ln \tan x\, dx=G</math>, <math>G</math>는 [[카탈란 상수]]:<math>\int_{0}^{\pi/4} \ln \tan x\,dx=-G</math>
-:<math>\int_{\pi/4}^{\pi/2} \ln \ln \tan x\, dx=\frac{\pi}{2}\ln \left(\frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{1}{4})}\sqrt{2\pi}\right)</math>:<math>\int_{0}^{\pi} (\ln \tan \frac{x}{4})^2\,dx=\frac{\pi^3}{4}</math>:<math>\int_0^{\infty}\frac{(\ln x)^2}{1+x^2} dx =\int_{0}^{\pi/2}(\ln \tan x)^2\,dx = \frac{ \pi^3}{8}</math><br>
+:<math>\int_{\pi/4}^{\pi/2} \ln \ln \tan x\, dx=\frac{\pi}{2}\ln \left(\frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{1}{4})}\sqrt{2\pi}\right)</math>:<math>\int_{0}^{\pi} (\ln \tan \frac{x}{4})^2\,dx=\frac{\pi^3}{4}</math>:<math>\int_0^{\infty}\frac{(\ln x)^2}{1+x^2} dx =\int_{0}^{\pi/2}(\ln \tan x)^2\,dx = \frac{ \pi^3}{8}</math>
-* ''''''[Vardi1988] '''참조'''<br>
+* ''''''[Vardi1988] '''참조'''
-*  적분:<math>\int_{0}^{\infty}\frac{\ln(x^{2}+1)}{x^{2}+1}\,dx=\pi\ln2</math> 에 대해서는 [[로그함수와 유리함수가 있는 정적분]]<br>
+*  적분:<math>\int_{0}^{\infty}\frac{\ln(x^{2}+1)}{x^{2}+1}\,dx=\pi\ln2</math> 에 대해서는 [[로그함수와 유리함수가 있는 정적분]]
@@ 111번째 줄: / 111번째 줄: @@
 ==메모==
 <math>f</math>가 <math>f(3)=-1</math>인 주기가 4인 디리클레 캐릭터라고 하면, <math>p(z)=z-z^3</math>
-다음의 $L$-함수
+다음의 <math>L</math>-함수
 :<math>L(s) = \sum_{n\geq 1}\frac{f(n)}{n^s}</math>
 는 아래의 식을 만족한다
@@ 126번째 줄: / 126번째 줄: @@
 * http://math.stackexchange.com/questions/285671/vardis-integral-int-pi-4-pi-2-ln-ln-tan-xdx
 <math>\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=L_{-7}(2)=1.15192547054449\cdots</math>
-* http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.0356v1.pdf<br>
+* http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.0356v1.pdf
@@ 136번째 줄: / 136번째 줄: @@
 ==개요==
-* [[등차수열의 소수분포에 관한 디리클레 정리]]<br>
+* [[등차수열의 소수분포에 관한 디리클레 정리]]
-* [[L-함수, 제타함수와 디리클레 급수|디리클레 급수]]<br>
+* [[L-함수, 제타함수와 디리클레 급수|디리클레 급수]]
-* [[후르비츠 제타함수(Hurwitz zeta function)|Hurwitz 제타함수]]<br>
+* [[후르비츠 제타함수(Hurwitz zeta function)|Hurwitz 제타함수]]
-* [[감마함수]]<br>
+* [[감마함수]]
-* [[다이로그 함수(dilogarithm)|다이로그 함수(dilogarithm )]]<br>
+* [[다이로그 함수(dilogarithm)|다이로그 함수(dilogarithm )]]
-* [[란덴변환(Landen's transformation)]]<br>
+* [[란덴변환(Landen's transformation)]]
-* [[르장드르 카이 함수]]<br>
+* [[르장드르 카이 함수]]
-* [[모듈라 군, j-invariant and the singular moduli]]<br>
+* [[모듈라 군, j-invariant and the singular moduli]]
-* [[카탈란 상수]]<br>
+* [[카탈란 상수]]
@@ 152번째 줄: / 152번째 줄: @@
 ==수학용어번역==
-* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
+* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
@@ 163번째 줄: / 163번째 줄: @@
 * https://docs.google.com/file/d/0B8XXo8Tve1cxNmRFU0Vyak14NGM/edit
-* [http://www.wolframalpha.com/input/?i=integrate_0%5E%28pi%29+x+cos+x+%2F%281%2Bsin%5E2+x%29 http://www.wolframalpha.com/input/?i=integrate_0^(pi)+x+cos+x+%2F(1%2Bsin^2+x)]<br>
+* [http://www.wolframalpha.com/input/?i=integrate_0%5E%28pi%29+x+cos+x+%2F%281%2Bsin%5E2+x%29 http://www.wolframalpha.com/input/?i=integrate_0^(pi)+x+cos+x+%2F(1%2Bsin^2+x)]
-* [http://www.wolframalpha.com/input/?i=log%5E2+%281%2Bsqrt%282%29%29+-pi%5E2%2F4 http://www.wolframalpha.com/input/?i=log^2+(1%2Bsqrt(2))+-pi^2%2F4]<br>
+* [http://www.wolframalpha.com/input/?i=log%5E2+%281%2Bsqrt%282%29%29+-pi%5E2%2F4 http://www.wolframalpha.com/input/?i=log^2+(1%2Bsqrt(2))+-pi^2%2F4]
-* [http://www.wolframalpha.com/input/?i=integrate+%28tan+x%2B1%29/sqrt%28tan%5E2+x+%2B1%29dx http://www.wolframalpha.com/input/?i=integrate+(tan+x%2B1)/sqrt(tan^2+x+%2B1)dx]<br>
+* [http://www.wolframalpha.com/input/?i=integrate+%28tan+x%2B1%29/sqrt%28tan%5E2+x+%2B1%29dx http://www.wolframalpha.com/input/?i=integrate+(tan+x%2B1)/sqrt(tan^2+x+%2B1)dx]
-* [http://www.wolframalpha.com/input/?i=integrate+%28tan+x-1%29/sqrt%28tan%5E2+x+%2B1%29dx http://www.wolframalpha.com/input/?i=integrate+(tan+x-1)/sqrt(tan^2+x+%2B1)dx]<br>
+* [http://www.wolframalpha.com/input/?i=integrate+%28tan+x-1%29/sqrt%28tan%5E2+x+%2B1%29dx http://www.wolframalpha.com/input/?i=integrate+(tan+x-1)/sqrt(tan^2+x+%2B1)dx]
@@ 185번째 줄: / 185번째 줄: @@
 ==관련논문==
-* [http://dx.doi.org/10.1007/s11040-010-9074-y Alternative Evaluation of a ln tan Integral Arising in Quantum Field Theory]<br>
+* [http://dx.doi.org/10.1007/s11040-010-9074-y Alternative Evaluation of a ln tan Integral Arising in Quantum Field Theory]
-**  Mark W. Coffey, Mathematical Physics, Analysis and Geometry, Volume 13, Number 2, 2010<br>
+**  Mark W. Coffey, Mathematical Physics, Analysis and Geometry, Volume 13, Number 2, 2010
-* '''[BBBZ2010]'''[http://arxiv.org/abs/1005.0414 Experimental Mathematics and Mathematical Physics]<br>
+* '''[BBBZ2010]'''[http://arxiv.org/abs/1005.0414 Experimental Mathematics and Mathematical Physics]
 ** DH Bailey, JM Borwein, D Broadhurst, W Zudilin, 2010
-* [http://www.springerlink.com/content/p2k0106727416271/?p=03915f5244d74523b6d36406299c80d5&pi=6 A class of logarithmic integrals]<br>
+* [http://www.springerlink.com/content/p2k0106727416271/?p=03915f5244d74523b6d36406299c80d5&pi=6 A class of logarithmic integrals]
 ** Luis A. Medina and Victor H. Moll, The Ramanujan Journal, Volume 20, Number 1 / 2009년 10월
-* [http://link.aip.org/link/?JMAPAQ/49/093508/1 Evaluation of a ln tan integral arising in quantum field theory]<br>
+* [http://link.aip.org/link/?JMAPAQ/49/093508/1 Evaluation of a ln tan integral arising in quantum field theory]
 ** Mark W. Coffey, J. Math. Phys. 49, 093508 (2008)
-* '''[Borwein and Boradhurst 1998]'''[http://arxiv.org/abs/hep-th/9811173 Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links]<br>
+* '''[Borwein and Boradhurst 1998]'''[http://arxiv.org/abs/hep-th/9811173 Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links]
 ** J.M. Borwein, D.J. Broadhurst, 1998
-* [http://doi.acm.org/10.1145/258726.258736 A class of logarithmic integrals]<br>
+* [http://doi.acm.org/10.1145/258726.258736 A class of logarithmic integrals]
 ** Victor Adamchik, 1997
-* '''[Vardi1988]'''[http://www.jstor.org/stable/2323562 Integrals, an Introduction to Analytic Number Theory]<br>
+* '''[Vardi1988]'''[http://www.jstor.org/stable/2323562 Integrals, an Introduction to Analytic Number Theory]
 ** Ilan Vardi, The American Mathematical Monthly, Vol. 95, No. 4 (Apr., 1988), pp. 308-315
@@ 206번째 줄: / 206번째 줄: @@
 ==관련도서==
-* [http://www.amazon.com/Irresistible-Integrals-Symbolics-Experiments-Evaluation/dp/0521796369 Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals]<br>
+* [http://www.amazon.com/Irresistible-Integrals-Symbolics-Experiments-Evaluation/dp/0521796369 Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals]
 ** George Boros and Victor Moll
 [[분류:적분]]

@@ 122번째 줄: / 122번째 줄: @@
 \end{align}
 </math>
 * http://math.stackexchange.com/questions/285671/vardis-integral-int-pi-4-pi-2-ln-ln-tan-xdx

@@ 110번째 줄: / 110번째 줄: @@
 ==메모==
 * http://math.stackexchange.com/questions/285671/vardis-integral-int-pi-4-pi-2-ln-ln-tan-xdx
 <math>\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=L_{-7}(2)=1.15192547054449\cdots</math>

← 이전 판		2013년 2월 11일 (월) 16:12 판
194번째 줄:		194번째 줄:
	* [http://www.amazon.com/Irresistible-Integrals-Symbolics-Experiments-Evaluation/dp/0521796369 Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals]<br>		* [http://www.amazon.com/Irresistible-Integrals-Symbolics-Experiments-Evaluation/dp/0521796369 Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals]<br>
	** George Boros and Victor Moll		** George Boros and Victor Moll
		+	[[분류:적분]]

← 이전 판		2013년 1월 28일 (월) 22:14 판
1번째 줄:		1번째 줄:
−	~~==이 항목의 수학노트 원문주소==~~
−
−	* [[로그 탄젠트 적분(log tangent integral)]]
−
−
−
−
−
	==개요==		==개요==

← 이전 판		2013년 1월 14일 (월) 22:55 판
111번째 줄:		111번째 줄:
	==역사==		==역사==

−	* [[~~수학사연표 (역사)\|수학사연표~~]]	+	* [[수학사 연표]]