List of special functions and eponyms

A

• Niels Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomial
• Sir George Biddell Airy: Airy function
• Waleed Al-Salam : 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 : Appell hypergeometric series, Appell polynomial, Generalized Appell polynomials
• Richard Askey: Askey–Wilson polynomial, Askey–Wilson function

  B

• 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
• Buchstab function
• Burchnall, Chaundy: Burchnall–Chaundy polynomial

  C

• 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

  D

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

  E

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

  F

• V. N. Faddeeva: Faddeeva function

  G

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

  H

• Wolfgang Hahn: Hahn polynomial, 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 : Heun's equation
• J. Horn: Horn hypergeometric series
• Adolf Hurwitz: Hurwitz zeta-function

  I

J

• Henry Jack Dundee: Jack polynomial
• F. H. Jackson: Jackson derivative Jackson integral
• Carl Gustav Jakob Jacobi: Jacobi polynomial

  K

• Joseph Marie Kampe de Feriet : 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

  L

• Edmond Laguerre: Laguerre polynomials
• Johann Heinrich Lambert: Lambert W function
• Gabriel Lamé: Lamé polynomial
• G. Lauricella Lauricella-Saran: Lauricella hypergeometric series
• Adrien-Marie Legendre: Legendre polynomials
• Eugen Cornelius Joseph von Lommel, physicist: Lommel polynomial, Lommel function, Lommel–Weber function

  M

• 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 : 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

  P

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

  R

• 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

  S

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

  T

• Francesco Tricomi: Tricomi–Carlitz polynomial

  W

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

  Z

• Frits Zernike: Zernike polynomials