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* Ehrenpreis, Leon. 2010. “Special Functions.” Inverse Problems and Imaging 4 (4): 639–47. doi:10.3934/ipi.2010.4.639. | * Ehrenpreis, Leon. 2010. “Special Functions.” Inverse Problems and Imaging 4 (4): 639–47. doi:10.3934/ipi.2010.4.639. | ||
* [http://www.stephenwolfram.com/publications/recent/specialfunctions/ The History and Future of Special Functions] Stephen Wolfram, 2005 | * [http://www.stephenwolfram.com/publications/recent/specialfunctions/ The History and Future of Special Functions] Stephen Wolfram, 2005 | ||
| + | * Kalnins, [http://www.revistas.unal.edu.co/index.php/recolma/article/viewFile/33654/33627 Special functions, Lie theory and partial differential equations], 1997 | ||
* Kirillov, A. A., & Etingof, P. I. I. (1994). A unified representation-theoretic approach to special functions. Functional Analysis and Its Applications, 28(1), 73-76. | * Kirillov, A. A., & Etingof, P. I. I. (1994). A unified representation-theoretic approach to special functions. Functional Analysis and Its Applications, 28(1), 73-76. | ||
* [http://www.jstor.org/stable/2321202 Ramanujan's Extensions of the Gamma and Beta Functions] Richard Askey, <cite>The American Mathematical Monthly</cite>, Vol. 87, No. 5 (May, 1980), pp. 346-359 | * [http://www.jstor.org/stable/2321202 Ramanujan's Extensions of the Gamma and Beta Functions] Richard Askey, <cite>The American Mathematical Monthly</cite>, Vol. 87, No. 5 (May, 1980), pp. 346-359 | ||
2014년 5월 3일 (토) 06:42 판
개요
- 직교다항식(orthogonal polynomials)
- 직교성과 완비성
- 3항 점화식 (3-term recurrence relation) 연분수와 관계
- 삼각함수 곱셈공식의 일반화 linearization of products
- 스텀-리우빌 문제
관련된 학부 과목과 미리 알고 있으면 좋은 것들
하위페이지
- 셀베르그 적분(Selberg integral)
- 구면조화함수(spherical harmonics)
- 르장드르 다항식
- 에르미트 다항식(Hermite polynomials)
- 오일러 베타적분
- 체비셰프 다항식
초등함수
직교다항식
- 자코비 다항식
- 구면조화함수(spherical harmonics)
- 라게르 다항식
- 윌슨 다항식
- 게겐바워 다항식(ultraspherical polynomials)
초기하함수
L-함수와 제타함수
타원적분과 타원함수
- 자코비 세타함수
- 타원함수
- 바이어슈트라스의 타원함수
- 타원적분
- 제1종타원적분 K (complete elliptic integral of the first kind)
- 베르누이 수와 베르누이 다항식
메모
- Difference Equations, Continued Fractions, and Orthogonal Polynomials (Walk Into a Bar) http://math.illinoisstate.edu/schebol/algebra-seminar-files/ortho.pdf
- Why is electrostatics in the complex plane interesting from a mathematical point of view?
- http://www.maths.leeds.ac.uk/~kisilv/courses/sp-funct.pdf
- 감마함수
- Digamma 함수
- 오일러 베타적분(베타함수)
관련된 항목들
리뷰, 에세이, 강의노트
- Wasson and Gilmore, “An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics.”
- Ehrenpreis, Leon. 2010. “Special Functions.” Inverse Problems and Imaging 4 (4): 639–47. doi:10.3934/ipi.2010.4.639.
- The History and Future of Special Functions Stephen Wolfram, 2005
- Kalnins, Special functions, Lie theory and partial differential equations, 1997
- Kirillov, A. A., & Etingof, P. I. I. (1994). A unified representation-theoretic approach to special functions. Functional Analysis and Its Applications, 28(1), 73-76.
- Ramanujan's Extensions of the Gamma and Beta Functions Richard Askey, The American Mathematical Monthly, Vol. 87, No. 5 (May, 1980), pp. 346-359