User:Charles Matthews/Special functions & eponyms

This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematic eponym). Named symmetric functions, 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