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* Dimitrov, Dimitar, and Yuan Xu. “Slater Determinants of Orthogonal Polynomials.” arXiv:1412.0326 [math-Ph], November 30, 2014. http://arxiv.org/abs/1412.0326. | * Dimitrov, Dimitar, and Yuan Xu. “Slater Determinants of Orthogonal Polynomials.” arXiv:1412.0326 [math-Ph], November 30, 2014. http://arxiv.org/abs/1412.0326. | ||
* Jafarov, E. I., N. I. Stoilova, and J. Van der Jeugt. ‘On a Pair of Difference Equations for the $_4F_3$ Type Orthogonal Polynomials and Related Exactly-Solvable Quantum Systems’. arXiv:1411.6125 [math-Ph], 22 November 2014. http://arxiv.org/abs/1411.6125. | * Jafarov, E. I., N. I. Stoilova, and J. Van der Jeugt. ‘On a Pair of Difference Equations for the $_4F_3$ Type Orthogonal Polynomials and Related Exactly-Solvable Quantum Systems’. arXiv:1411.6125 [math-Ph], 22 November 2014. http://arxiv.org/abs/1411.6125. | ||
| + | [[분류:특수함수]] | ||
2015년 3월 29일 (일) 20:55 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
초등함수
직교다항식
- 자코비 다항식
- 체비셰프 다항식
- 르장드르 다항식
- 라게르 다항식
- 게겐바워 다항식(ultraspherical polynomials)
- 에르미트 다항식(Hermite polynomials)
- 윌슨 다항식
- 구면조화함수(spherical harmonics)
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, Ryan D., and Robert Gilmore. 2013. “An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics.” arXiv:1309.2544 [math-Ph], September. http://arxiv.org/abs/1309.2544.
- 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
- Koekoek, Roelof, and Rene F. Swarttouw. "The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue." arXiv preprint math/9602214 (1996). http://arxiv.org/abs/math/9602214
- 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.
관련논문
- Borzov, V. V., and E. V. Damaskinsky. ‘Comment on “On the Dimensions of the Oscillator Algebras Induced by Orthogonal Polynomials” [J. Math. Phys. {\bf 55}, 093511 (2014)]’. arXiv:1503.08202 [math-Ph], 27 March 2015. http://arxiv.org/abs/1503.08202.
- Honnouvo, G., and K. Thirulogasanthar. ‘On the Dimensions of the Oscillator Algebras Induced by Orthogonal Polynomials’. arXiv:1305.2509 [math-Ph], 11 May 2013. http://arxiv.org/abs/1305.2509.
- Dimitrov, Dimitar, and Yuan Xu. “Slater Determinants of Orthogonal Polynomials.” arXiv:1412.0326 [math-Ph], November 30, 2014. http://arxiv.org/abs/1412.0326.
- Jafarov, E. I., N. I. Stoilova, and J. Van der Jeugt. ‘On a Pair of Difference Equations for the $_4F_3$ Type Orthogonal Polynomials and Related Exactly-Solvable Quantum Systems’. arXiv:1411.6125 [math-Ph], 22 November 2014. http://arxiv.org/abs/1411.6125.