"리만 미분방정식"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| 9번째 줄: | 9번째 줄: | ||
==개요== | ==개요== | ||
| − | * <math>a,b,c</math> 세 점에서 [[정규특이점(regular singular points)|정규특이점]]을 가지는 이계선형미분방정식:<math>\frac{d^2w}{dz^2} + \left[ \frac{1-\alpha-\alpha'}{z-a} + \frac{1-\beta-\beta'}{z-b} + \frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}+\left[ \frac{\alpha\alpha' (a-b)(a-c)} {z-a} +\frac{\beta\beta' (b-c)(b-a)} {z-b} +\frac{\gamma\gamma' (c-a)(c-b)} {z-c} \right] \frac{w}{(z-a)(z-b)(z-c)}=0</math | + | * <math>a,b,c</math> 세 점에서 [[정규특이점(regular singular points)|정규특이점]]을 가지는 이계선형미분방정식:<math>\frac{d^2w}{dz^2} + \left[ \frac{1-\alpha-\alpha'}{z-a} + \frac{1-\beta-\beta'}{z-b} + \frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}+\left[ \frac{\alpha\alpha' (a-b)(a-c)} {z-a} +\frac{\beta\beta' (b-c)(b-a)} {z-b} +\frac{\gamma\gamma' (c-a)(c-b)} {z-c} \right] \frac{w}{(z-a)(z-b)(z-c)}=0</math> 여기서 <math>\alpha+\alpha'+\beta+\beta'+\gamma+\gamma'=1</math> |
* [[초기하 미분방정식(Hypergeometric differential equations)]]의 일반화 | * [[초기하 미분방정식(Hypergeometric differential equations)]]의 일반화 | ||
| − | * 해는 리만의 P-함수로 주어진다:<math>w(z)=P \left\{ \begin{matrix} a & b & c & \; \\ \alpha & \beta & \gamma & z \ \alpha' & \beta' & \gamma' & \; \end{matrix} \right\}</math | + | * 해는 리만의 P-함수로 주어진다:<math>w(z)=P \left\{ \begin{matrix} a & b & c & \; \\ \alpha & \beta & \gamma & z \ \alpha' & \beta' & \gamma' & \; \end{matrix} \right\}</math> |
* [http://www.maths.leeds.ac.uk/%7Ekisilv/courses/sp-funct.pdf http://www.maths.leeds.ac.uk/~kisilv/courses/sp-funct.pdf] | * [http://www.maths.leeds.ac.uk/%7Ekisilv/courses/sp-funct.pdf http://www.maths.leeds.ac.uk/~kisilv/courses/sp-funct.pdf] | ||
| 59번째 줄: | 59번째 줄: | ||
* http://www.google.com/dictionary?langpair=en|ko&q= | * http://www.google.com/dictionary?langpair=en|ko&q= | ||
| − | * [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=&fstr= 대한수학회 수학 학술 용어집] |
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ** 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] | * [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] | ||
| 74번째 줄: | 74번째 줄: | ||
* http://www.wolframalpha.com/input/?i= | * http://www.wolframalpha.com/input/?i= | ||
* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | ||
| − | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] |
** http://www.research.att.com/~njas/sequences/?q= | ** http://www.research.att.com/~njas/sequences/?q= | ||
| 83번째 줄: | 83번째 줄: | ||
==관련논문== | ==관련논문== | ||
| − | * On Riemann's equations which are solvable by quadrature | + | * On Riemann's equations which are solvable by quadrature |
** Kimura T 1969 | ** Kimura T 1969 | ||
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
[[분류:미분방정식]] | [[분류:미분방정식]] | ||
2020년 11월 13일 (금) 20:56 판
이 항목의 스프링노트 원문주소
개요
- \(a,b,c\) 세 점에서 정규특이점을 가지는 이계선형미분방정식\[\frac{d^2w}{dz^2} + \left[ \frac{1-\alpha-\alpha'}{z-a} + \frac{1-\beta-\beta'}{z-b} + \frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}+\left[ \frac{\alpha\alpha' (a-b)(a-c)} {z-a} +\frac{\beta\beta' (b-c)(b-a)} {z-b} +\frac{\gamma\gamma' (c-a)(c-b)} {z-c} \right] \frac{w}{(z-a)(z-b)(z-c)}=0\] 여기서 \(\alpha+\alpha'+\beta+\beta'+\gamma+\gamma'=1\)
- 초기하 미분방정식(Hypergeometric differential equations)의 일반화
- 해는 리만의 P-함수로 주어진다\[w(z)=P \left\{ \begin{matrix} a & b & c & \; \\ \alpha & \beta & \gamma & z \ \alpha' & \beta' & \gamma' & \; \end{matrix} \right\}\]
- http://www.maths.leeds.ac.uk/~kisilv/courses/sp-funct.pdf
재미있는 사실
역사
메모
관련된 항목들
수학용어번역
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://eom.springer.de/r/r081870.htm
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
- On Riemann's equations which are solvable by quadrature
- Kimura T 1969
- http://www.jstor.org/action/doBasicSearch?Query=
- http://dx.doi.org/