"직교다항식"의 두 판 사이의 차이
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==개요== | ==개요== | ||
| − | * 직교다항식(orthogonal polynomials) | + | * 직교다항식(orthogonal polynomials) |
** 직교성과 완비성 | ** 직교성과 완비성 | ||
| − | ** | + | ** 3항 점화식 (3-term recurrence relation) 연분수와 관계 |
| − | ** 삼각함수 곱셈공식의 | + | ** 삼각함수 곱셈공식의 일반화 linearization of products |
** 스텀-리우빌 문제 | ** 스텀-리우빌 문제 | ||
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| + | ===예=== | ||
* [[자코비 다항식]] | * [[자코비 다항식]] | ||
| − | * [[ | + | * [[체비셰프 다항식]] |
| − | * | + | * [[르장드르 다항식]] |
| + | * [[라게르 다항식]] | ||
| + | * [[게겐바워 다항식(ultraspherical polynomials)]] | ||
| + | * [[에르미트 다항식(Hermite polynomials)]] | ||
* 윌슨 다항식 | * 윌슨 다항식 | ||
| − | * | + | * [[로저스-세괴 다항식 (Rogers-Szegő polynomials)]] |
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| + | ==메모== | ||
| + | * Difference Equations, Continued Fractions, and Orthogonal Polynomials (Walk Into a Bar) http://math.illinoisstate.edu/schebol/algebra-seminar-files/ortho.pdf | ||
| + | * [http://www.math.u-szeged.hu/%7Ebaloghf/homepage/talks/ism_conf_2007.pdf Why is electrostatics in the complex plane interesting from a mathematical point of view?] | ||
| + | * [http://www.maths.leeds.ac.uk/%7Ekisilv/courses/sp-funct.pdf http://www.maths.leeds.ac.uk/~kisilv/courses/sp-funct.pdf] | ||
* [[감마함수]] | * [[감마함수]] | ||
* [[다이감마 함수(digamma function)|Digamma 함수]] | * [[다이감마 함수(digamma function)|Digamma 함수]] | ||
| − | * [[오일러 베타적분(베타함수) | + | * [[오일러 베타적분(베타함수)]] |
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==관련된 항목들== | ==관련된 항목들== | ||
| − | + | * [[공대수 (coalgebra)]] | |
| − | * [[다이로그 함수(dilogarithm) | + | * [[다이로그 함수(dilogarithm)]] |
* [[삼각함수에는 왜 공식이 많은가?]] | * [[삼각함수에는 왜 공식이 많은가?]] | ||
* [[오일러(1707-1783)]] | * [[오일러(1707-1783)]] | ||
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| − | + | ==메모== | |
| + | * Dumitriu, Ioana, Alan Edelman, and Gene Shuman. “MOPS: Multivariate Orthogonal Polynomials (symbolically).” arXiv:math-ph/0409066, September 23, 2004. http://arxiv.org/abs/math-ph/0409066. | ||
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| + | ==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. | ||
| + | * [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 | ||
| + | * 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. | ||
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==관련논문== | ==관련논문== | ||
| − | + | * Koornwinder, Tom H. “Quadratic Transformations for Orthogonal Polynomials in One and Two Variables.” arXiv:1512.09294 [math], December 31, 2015. http://arxiv.org/abs/1512.09294. | |
| − | * [http:// | + | * Odake, Satoru. “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III.” arXiv:1509.08213 [hep-Th, Physics:math-Ph, Physics:nlin], September 28, 2015. http://arxiv.org/abs/1509.08213. |
| − | * [http:// | + | * 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 <math>_4F_3</math> 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]] | ||
2020년 12월 28일 (월) 03:57 기준 최신판
개요
- 직교다항식(orthogonal polynomials)
- 직교성과 완비성
- 3항 점화식 (3-term recurrence relation) 연분수와 관계
- 삼각함수 곱셈공식의 일반화 linearization of products
- 스텀-리우빌 문제
예
- 자코비 다항식
- 체비셰프 다항식
- 르장드르 다항식
- 라게르 다항식
- 게겐바워 다항식(ultraspherical polynomials)
- 에르미트 다항식(Hermite polynomials)
- 윌슨 다항식
- 로저스-세괴 다항식 (Rogers-Szegő polynomials)
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
메모
- Dumitriu, Ioana, Alan Edelman, and Gene Shuman. “MOPS: Multivariate Orthogonal Polynomials (symbolically).” arXiv:math-ph/0409066, September 23, 2004. http://arxiv.org/abs/math-ph/0409066.
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
- Koornwinder, Tom H. “Quadratic Transformations for Orthogonal Polynomials in One and Two Variables.” arXiv:1512.09294 [math], December 31, 2015. http://arxiv.org/abs/1512.09294.
- Odake, Satoru. “Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III.” arXiv:1509.08213 [hep-Th, Physics:math-Ph, Physics:nlin], September 28, 2015. http://arxiv.org/abs/1509.08213.
- 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.