List of special functions and eponyms

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description: ANiels Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomialSir George Biddell Airy: Airy functionWaleed Al-Salam (1926–1996): Al-Salam polynomial - Al Salam–Carlit ...

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)

Ernest William Barnes: Barnes G-function
E. T. Bell: Bell polynomials
Bender–Dunne polynomial
Jacob Bernoulli: Bernoulli polynomial
Friedrich Bessel: Bessel function, Bessel–Clifford function
H. Blasius: Blasius functions
R. P. Boas, R. C. Buck: Boas–Buck polynomial
Böhmer integral
de Bruijn function
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
Cyclotomic polynomials

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

Wolfgang Hahn: Hahn polynomial, (with H. Exton) Hahn–Exton Bessel function
Philip Hall: Hall polynomial, Hall–Littlewood polynomial
Hermann Hankel: Hankel function
Heine: Heine functions
Charles Hermite: Hermite polynomials
Karl L. W. M. Heun (1859 – 1929): Heun's equation
J. Horn: Horn hypergeometric series
Adolf Hurwitz: Hurwitz zeta-function


Henry Jack (1917–1978) Dundee: Jack polynomial
F. H. Jackson: Jackson derivative Jackson integral
Carl Gustav Jakob 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
Mikhail Kravchuk: Kravchuk polynomial

Edmond Laguerre: Laguerre polynomials
Gabriel 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, Lommel–Weber function

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, Meier function
Meijer G-function
Josef Meixner: Meixner polynomial, Meixner-Pollaczek polynomial
Mittag-Leffler: Mittag-Leffler polynomials
Mott polynomial

Paul Painlevé: Painlevé function, Painlevé transcendents
Poisson–Charlier polynomial
Pollaczek 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–Szegö polynomial

Schubert polynomial
Issai Schur: Schur polynomial
Atle Selberg: Selberg integral
Sheffer polynomial
Slater's identities
Thomas Joannes Stieltjes: Stieltjes polynomial, Stieltjes–Wigert polynomials
Stromgen function
Hermann Struve: Struve function

Francesco Tricomi: Tricomi–Carlitz polynomial

Wall polynomial
Wangerein: Wangerein functions
Weber function
Weierstrass: Weierstrass function
Louis Weisner: Weisner's method
E. T. Whittaker: Whittaker function
Wilson polynomial

Frits Zernike: Zernike polynomials

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