"자코비 타원함수"의 두 판 사이의 차이
Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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==개요== | ==개요== | ||
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<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> | ||
| 49번째 줄: | 40번째 줄: | ||
* [[렘니스케이트(lemniscate) 곡선의 길이와 타원적분]] | * [[렘니스케이트(lemniscate) 곡선의 길이와 타원적분]] | ||
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| 73번째 줄: | 48번째 줄: | ||
* https://docs.google.com/file/d/0B8XXo8Tve1cxeVNacEtlVGlYeU0/edit | * https://docs.google.com/file/d/0B8XXo8Tve1cxeVNacEtlVGlYeU0/edit | ||
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| − | == | + | ==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. | |
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2015년 10월 22일 (목) 22:31 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
\(\begin{align}\operatorname{cn}(x+y) & ={\operatorname{cn}(x)\;\operatorname{cn}(y)- \operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{dn}(x)\;\operatorname{dn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x) \;\operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{sn}(x+y) & ={\operatorname{sn}(x)\;\operatorname{cn}(y)\;\operatorname{dn}(y) +\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{dn}(x)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}, \\[8pt]\operatorname{dn}(x+y) & ={\operatorname{dn}(x)\;\operatorname{dn}(y)- k^2 \;\operatorname{sn}(x)\;\operatorname{sn}(y)\;\operatorname{cn}(x)\;\operatorname{cn}(y)\over {1 - k^2 \;\operatorname{sn}^2 (x)\; \operatorname{sn}^2 (y)}}.\end{align}\)
역사
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.