"직교다항식"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
 
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3번째 줄: 3번째 줄:
 
*  직교다항식(orthogonal polynomials)
 
*  직교다항식(orthogonal polynomials)
 
** 직교성과 완비성
 
** 직교성과 완비성
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** 3항 점화식 (3-term recurrence relation) 연분수와 관계
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** 3항 점화식 (3-term recurrence relation) 연분수와 관계
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** 삼각함수 곱셈공식의 일반화 linearization of products
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** 삼각함수 곱셈공식의 일반화 linearization of products
 
** 스텀-리우빌 문제
 
** 스텀-리우빌 문제
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==관련된 학부 과목과 미리 알고 있으면 좋은 것들==
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===예===
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* [[자코비 다항식]]
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* [[일변수미적분학]]
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* [[체비셰프 다항식]]
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* [[복소함수론]]
 
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* [[푸리에 해석]]
 
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* [[상미분방정식]]
 
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* 편미분방정식
 
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== 하위페이지 ==
 
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* [[셀베르그 적분(Selberg integral)]]
 
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* [[구면조화함수(spherical harmonics)]]
 
 
* [[르장드르 다항식]]
 
* [[르장드르 다항식]]
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* [[라게르 다항식]]
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* [[게겐바워 다항식(ultraspherical polynomials)]]
 
* [[에르미트 다항식(Hermite polynomials)]]
 
* [[에르미트 다항식(Hermite polynomials)]]
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* [[오일러 베타적분(베타함수)|오일러 베타적분]]
 
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* [[체비셰프 다항식]]
 
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===초등함수===
 
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* [[삼각함수]]
 
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* [[로그 함수]]
 
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* [[지수함수]]
 
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===직교다항식===
 
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* [[자코비 다항식]]
 
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* [[구면조화함수(spherical harmonics)]]
 
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* 라게르 다항식
 
 
* 윌슨 다항식
 
* 윌슨 다항식
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* 게겐바워 다항식(ultraspherical polynomials)
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* [[로저스-세괴 다항식 (Rogers-Szegő polynomials)]]
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===초기하함수===
 
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* [[초기하급수(Hypergeometric series)]]
 
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* [[오일러-가우스 초기하함수2F1]]
 
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* [[Q-초기하급수(q-hypergeometric series)와 양자미적분학(q-calculus)]]
 
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===L-함수와 제타함수===
 
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* [[L-함수, 제타함수와 디리클레 급수]]
 
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* [[리만제타함수|리만제타함수와 리만가설]]
 
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* [[디리클레 베타함수]]
 
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===타원적분과 타원함수===
 
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* [[자코비 세타함수]]
 
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* [[타원함수]]
 
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* [[바이어슈트라스 타원함수 ℘|바이어슈트라스의 타원함수]]
 
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* [[타원적분]]
 
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* [[제1종타원적분 K (complete elliptic integral of the first kind)]]
 
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* [[베르누이 수|베르누이 수와 베르누이 다항식]]
 
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96번째 줄: 36번째 줄:
 
* [[오일러(1707-1783)]]
 
* [[오일러(1707-1783)]]
  
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==메모==
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* 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.
  
  
103번째 줄: 46번째 줄:
 
* [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
 
* Kalnins, [http://www.revistas.unal.edu.co/index.php/recolma/article/viewFile/33654/33627 Special functions, Lie theory and partial differential equations], 1997
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* 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.
 
* 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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* [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
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==관련논문==
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* 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.
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* 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.
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* 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.
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* 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.
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[[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


메모


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.
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