View source for User:Charles Matthews/Special functions & eponyms

This is a '''list of special function eponyms''' in [[mathematics]], to cover the theory of [[special function]]s, the [[differential equation]]s they satisfy, named [[differential operator]]s of the theory (but not intended to include every mathematic [[eponym]]). Named [[symmetric function]]s, and more general special polynomials, are included. 

==[[Niels Abel]]==
*[[Abel polynomials]] - [[Abelian function]] - [[Abel-Gontscharoff interpolating polynomial]]

==[[Sir George Biddell Airy]]==
*[[Airy function]] 

==[[Waleed Al-Salam]] (1926-1996)==
*[[Al-Salam polynomial]] - [[Al Salam-Carlitz polynomial]] - [[Al Salam-Chihara polynomial]]

==[[C. T. Anger]]==
*[[Anger-Weber function]] 

==[[Kazuhiko Aomoto]]==
*[[Aomoto-Gel'fand hypergeometric function]] - [[Aomoto integral]] 

==[[Paul Emile Appell]] (1855-1930)==  
*[[Appell hypergeometric series]] - [[Appell polynomial]]

==[[Richard Askey]]==
*[[Askey-Wilson polynomial]], [[Askey-Wilson function]] (with [[James Wilson]])

==[[E. T. Bell]]==
*[[Bell polynomials]]

*[[Bender-Dunne polynomial]]

==[[Bernoulli]]==
*[[Bernoulli polynomial]]

==[[Bessel]]==
*[[Bessel function]]

==[[R. P. Boas]], [[R. C. Buck]]==
*[[Boas-Buck polynomial]]
 
*[[Boehmer integral]]

==[[Burchnall]], [[Chaundy]]==
*[[Burchnall-Chaundy polynomial]]

==[[Leonard Carlitz]]==
*[[Carlitz polynomial]]

==[[Arthur Cayley]], [[Capelli]]==
*[[Cayley-Capelli operator]]

*[[Celine's polynomial]]

*[[Charlier polynomial]]

==[[Pafnuty Chebyshev]]==
*[[Chebyshev polynomials]]

==[[Christoffel]], [[Darboux]]==
*[[Christoffel-Darboux relation]]

==[[Charles F. Dunkl]]==
*[[Dunkl operator]], [[Jacobi-Dunkl operator]], [[Dunkl–Cherednik operator]]

==[[Engel]]==
*[[Engel series]]

==[[Erdélyi Artúr]]==
*[[Erdelyi-Kober operator]] 

==[[Leonhard Euler]]==
*[[Euler polynomial]]

==[[C. F. Gauss]]==
*[[Gaussian polynomial]]

==[[Leopold Bernhard Gegenbauer]]==
*[[Gegenbauer polynomials]] 

*[[Gottlieb polynomial]]
*[[Gould polynomial]]

==[[Christoph Gudermann]]==
*[[Gudermannian function]]

*[[Hahn polynomial]]

==[[H. Exton]]==
*[[Hahn-Exton Bessel function]] 

*[[Hall polynomial]]
*[[Hall-Littlewood polynomial]]

==[[Hankel]]==
*[[Hankel function]]

==[[Charles Hermite]]==
*[[Hermite polynomials]]

==[[Karl L. W. M. Heun]](1859 - 1929)==
*[[Heun's equation]] 

==[[J. Horn]]==
*[[Horn hypergeometric series]] 

==[[Adolf Hurwitz]]==
*[[Hurwitz zeta-function]] 

*[[Ismaili polynomial]]

==[[Henry Jack]] (1917-1978) Dundee==
*[[Jack polynomial]] [[Henry Jack]] 

==[[F. H. Jackson]]==
*[[Jackson derivative]] [[Jackson integral]] 

==[[Jacobi]]==
*[[Jacobi polynomial]]

==[[Joseph Marie Kampe de Feriet]] (1893-1982)==
*[[Kampe de Feriet hypergeometric series]],

==[[David Kazhdan]], [[George Lusztig]]==
*[[Kazhdan-Lusztig polynomial]] 

==[[Lord Kelvin]]==
*[[Kelvin function]] 

*[[Kibble-Slepian formula]] 

==[[Kirchhoff]]==
*[[Kirchhoff polynomial]]

==[[Tom H. Koornwinder]]==
*[[Koornwinder polynomial]] 
 
*[[Kostka polynomial]]
*[[Kostka-Foulkes polynomial]]

==[[Mikhailo Pylypovich Kravchuk]]==
*[[Krawtchouk polynomial]] 

==[[Edmond Laguerre]]==
*[[Laguerre polynomials]]

==[[Lamé]]==
*[[Lamé polynomial]]

==[[G. Lauricella]] Lauricella-Saran==
*[[Lauricella hypergeometric series]] 

==[[Adrien-Marie Legendre]]==
*[[Legendre polynomials]]

==[[Eugen Cornelius Joseph von Lommel]] (1837-1899) physicist==
*[[Lommel polynomial]], [[Lommel function]] 

==[[Ian G. Macdonald]]==
*[[Macdonald polynomial]], [[Macdonald-Kostka polynomial]], [[Macdonald spherical function]]

*[[Mahler polynomial]]

*[[Maitland function]]

==[[Emile Léonard Mathieu]]==
*[[Mathieu function]] 

==[[F. G. Mehler]], student of Dirichlet (Ferdinand)==
*[[Mehler's formula]], [[Mehler-Fock formula]], [[Mehler-Heine formula]], [[Meier function]]

*[[Meijer G-function]]

==[[Josef Meixner]]==
*[[Meixner polynomial]],[[Meixner-Pollaczek polynomial]]

*[[Mittag-Leffler polynomial]]

*[[Mott polynomial]]

==[[Paul Painlevé]]==
*[[Painlevé function]] 

*[[Poisson-Charlier polynomial]]

*[[Pollaczek polynomial]]

==[[Giulio Racah]]==
*[[Racah polynomial]] *

==[[Riccati]]==
*[[Riccati-Bessel function]]

==[[Bernhard Riemann]]==
*[[Riemann zeta-function]] 

==[[Rodrigues]]==
*[[Rodrigues formula]]

==[[L. J. Rogers]] = [[Leonard James Rogers]]==
*[[Rogers-Askey- Ismail polynomial]], [[Rogers-Ramanujan identity]], [[Rogers-Szegö polynomial]]

*[[Schubert polynomial]]

==[[Issai Schur]]==
*[[Schur polynomial]] 

==[[Atle Selberg]]==
*[[Selberg integral]]

==[[Sheffer]]==
*[[Sheffer polynomial]]

*[[Slater's identities]]

==[[Stieltjes]]==
*[[Stieltjes polynomial]]
*[[Stieltjes-Wigert polynomial]]

*[[Stromgen function]]

==[[Hermann Struve]]==
*[[Struve function]] 

==[[F. G. Tricomi]]==
*[[Tricomi-Carlitz polynomial]] *[[Wall polynomial]]

*[[Weber function]]

==[[Louis Weisner]]==
*[[Weisner's method]] 

==[[E. T. Whittaker]]==
*[[Whittaker function]]

*[[Wilson polynomial]]