List of special functions and 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 mathematical eponym). Named symmetric functions, and other special polynomials, are included.

A

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 Émile Appell (1855–1930): Appell hypergeometric series, Appell polynomial, Generalized Appell polynomials
Richard Askey: Askey–Wilson polynomial, Askey–Wilson function (with James A. Wilson)

Leonard Carlitz: Carlitz polynomial
Arthur Cayley, Capelli: Cayley–Capelli operator
- Celine's polynomial
- Charlier polynomial
Pafnuty Chebyshev: Chebyshev polynomials
Elwin Bruno Christoffel, Darboux: Christoffel–Darboux relation
Cyclotomic polynomials

H. G. Dawson: Dawson function
Charles F. Dunkl: Dunkl operator, Jacobi–Dunkl operator, Dunkl–Cherednik operator
- Dickman–de Bruijn function

Engel: Engel expansion
Erdélyi Artúr: Erdelyi–Kober operator
Leonhard Euler: Euler polynomial, Eulerian integral, Euler hypergeometric integral

V. N. Faddeeva: Faddeeva function (also known as the complex error function; see error function)

C. F. Gauss: Gaussian polynomial, Gaussian distribution, etc.
Leopold Bernhard Gegenbauer: Gegenbauer polynomials
- Gottlieb polynomial
- Gould polynomial
Christoph Gudermann: Gudermannian function

I Function - V P Saxena 1982

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
Mikhail Kravchuk: Kravchuk polynomial

Ian G. Macdonald: Macdonald polynomial, Macdonald–Kostka polynomial, Macdonald spherical function
- Mahler polynomial
- Maitland function
Émile Léonard Mathieu: Mathieu function
F. G. Mehler, student of Dirichlet (Ferdinand): Mehler's formula, Mehler–Fock formula, Mehler–Heine formula, Mehler functions
- Meijer G-function
Josef Meixner: Meixner polynomial, Meixner-Pollaczek polynomial
Mittag-Leffler: Mittag-Leffler polynomials
- Mott polynomial

Giulio Racah: Racah polynomial
Jacopo Riccati: Riccati–Bessel function
Bernhard Riemann: Riemann zeta-function
Olinde Rodrigues: Rodrigues formula
Leonard James Rogers: Rogers–Askey–Ismail polynomial, Rogers–Ramanujan identity, Rogers–Szegő polynomials

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