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Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 13개는 보이지 않습니다) | |||
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| − | + | ==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> | ||
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| − | + | ==덧셈공식== | |
| − | + | <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== | |
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* Math Overflow http://mathoverflow.net/search?q= | * Math Overflow http://mathoverflow.net/search?q= | ||
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| − | + | ==관련된 항목들== | |
* [[렘니스케이트(lemniscate) 곡선의 길이와 타원적분]] | * [[렘니스케이트(lemniscate) 곡선의 길이와 타원적분]] | ||
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| − | + | ==매스매티카 파일 및 계산 리소스== | |
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* https://docs.google.com/file/d/0B8XXo8Tve1cxeVNacEtlVGlYeU0/edit | * https://docs.google.com/file/d/0B8XXo8Tve1cxeVNacEtlVGlYeU0/edit | ||
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| − | + | ==사전 형태의 자료== | |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| − | * http://en.wikipedia.org/wiki/ | + | * http://en.wikipedia.org/wiki/Jacobi_elliptic_functions |
* [http://eom.springer.de/default.htm The Online Encyclopaedia of Mathematics] | * [http://eom.springer.de/default.htm The Online Encyclopaedia of Mathematics] | ||
* [http://dlmf.nist.gov NIST Digital Library of Mathematical Functions] | * [http://dlmf.nist.gov NIST Digital Library of Mathematical Functions] | ||
* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] | * [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] | ||
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| − | < | + | ==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. | ||
| − | * | + | ==메타데이터== |
| − | + | ===위키데이터=== | |
| − | * | + | * ID : [https://www.wikidata.org/wiki/Q1473526 Q1473526] |
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'jacobi'}, {'LOWER': 'elliptic'}, {'LEMMA': 'function'}] | ||
2021년 2월 17일 (수) 04:57 기준 최신판
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.
메타데이터
위키데이터
- ID : Q1473526
Spacy 패턴 목록
- [{'LOWER': 'jacobi'}, {'LOWER': 'elliptic'}, {'LEMMA': 'function'}]