"자코비 타원함수"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| 2번째 줄: | 2번째 줄: | ||
<math>\text{sn}(z|-1)=z-\frac{z^5}{10}+\frac{z^9}{120}-\frac{11 z^{13}}{15600}+\frac{211 z^{17}}{3536000}+O\left(z^{21}\right)</math> | <math>\text{sn}(z|-1)=z-\frac{z^5}{10}+\frac{z^9}{120}-\frac{11 z^{13}}{15600}+\frac{211 z^{17}}{3536000}+O\left(z^{21}\right)</math> | ||
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==덧셈공식== | ==덧셈공식== | ||
| 10번째 줄: | 10번째 줄: | ||
<math>\begin{align}\operatorname{cn}(x+y) & ={\operatorname{cn}(x)\;\operatorname{cn}(y)- \operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{dn}(x)\;\operatorname{dn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x) \;\operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{sn}(x+y) & ={\operatorname{sn}(x)\;\operatorname{cn}(y)\;\operatorname{dn}(y) +\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{dn}(x)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{dn}(x+y) & ={\operatorname{dn}(x)\;\operatorname{dn}(y)- k^2 \;\operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{cn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}.\end{align}</math> | <math>\begin{align}\operatorname{cn}(x+y) & ={\operatorname{cn}(x)\;\operatorname{cn}(y)- \operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{dn}(x)\;\operatorname{dn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x) \;\operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{sn}(x+y) & ={\operatorname{sn}(x)\;\operatorname{cn}(y)\;\operatorname{dn}(y) +\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{dn}(x)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{dn}(x+y) & ={\operatorname{dn}(x)\;\operatorname{dn}(y)- k^2 \;\operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{cn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}.\end{align}</math> | ||
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==메모== | ==메모== | ||
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* Math Overflow http://mathoverflow.net/search?q= | * Math Overflow http://mathoverflow.net/search?q= | ||
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==관련된 항목들== | ==관련된 항목들== | ||
| 30번째 줄: | 30번째 줄: | ||
* [[렘니스케이트(lemniscate) 곡선의 길이와 타원적분]] | * [[렘니스케이트(lemniscate) 곡선의 길이와 타원적분]] | ||
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==매스매티카 파일 및 계산 리소스== | ==매스매티카 파일 및 계산 리소스== | ||
| 39번째 줄: | 39번째 줄: | ||
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| − | ==사전 | + | ==사전 형태의 자료== |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 49번째 줄: | 49번째 줄: | ||
* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] | * [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] | ||
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==관련논문== | ==관련논문== | ||
| − | * Kiselev, Oleg. “Uniform Asymptotic Behaviour of Jacobi-<math>\operatorname{sn}</math> near a Singular Point. The Lost Formula from Handbooks for Elliptic Functions.” arXiv:1510.06602 [nlin], October 22, 2015. http://arxiv.org/abs/1510.06602. | + | * Kiselev, Oleg. “Uniform Asymptotic Behaviour of Jacobi-<math>\operatorname{sn}</math> near a Singular Point. The Lost Formula from Handbooks for Elliptic Functions.” arXiv:1510.06602 [nlin], October 22, 2015. http://arxiv.org/abs/1510.06602. |
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2020년 12월 28일 (월) 03:53 판
개요
\(\text{sn}(z|-1)=z-\frac{z^5}{10}+\frac{z^9}{120}-\frac{11 z^{13}}{15600}+\frac{211 z^{17}}{3536000}+O\left(z^{21}\right)\)
덧셈공식
\(\begin{align}\operatorname{cn}(x+y) & ={\operatorname{cn}(x)\;\operatorname{cn}(y)- \operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{dn}(x)\;\operatorname{dn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x) \;\operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{sn}(x+y) & ={\operatorname{sn}(x)\;\operatorname{cn}(y)\;\operatorname{dn}(y) +\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{dn}(x)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{dn}(x+y) & ={\operatorname{dn}(x)\;\operatorname{dn}(y)- k^2 \;\operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{cn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}.\end{align}\)
메모
- Math Overflow http://mathoverflow.net/search?q=
관련된 항목들
매스매티카 파일 및 계산 리소스
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Jacobi_elliptic_functions
- The Online Encyclopaedia of Mathematics
- NIST Digital Library of Mathematical Functions
- The World of Mathematical Equations
관련논문
- Kiselev, Oleg. “Uniform Asymptotic Behaviour of Jacobi-\(\operatorname{sn}\) near a Singular Point. The Lost Formula from Handbooks for Elliptic Functions.” arXiv:1510.06602 [nlin], October 22, 2015. http://arxiv.org/abs/1510.06602.