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.
Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomial
Askey–Wilson polynomial, Askey–Wilson function (with James A. Wilson)
Bernoulli polynomial
Carlitz polynomial
Dunkl operator, Jacobi–Dunkl operator, Dunkl–Cherednik operator
Euler polynomial, Eulerian integral, Euler hypergeometric integral
Gaussian polynomial, Gaussian distribution, Hypergeometric function 2F1, etc.
Hall polynomial, Hall–Littlewood polynomial
Hurwitz zeta-function
Jacobi polynomial, Jacobi theta function
Kirchhoff polynomial
Kravchuk polynomial
Lamé polynomial
Macdonald polynomial, Macdonald–Kostka polynomial, Macdonald spherical function
Meixner polynomial, Meixner-Pollaczek polynomial
Painlevé function, Painlevé transcendents
Racah polynomial
Riccati–Bessel function
Rodrigues formula
Rogers–Askey–Ismail polynomial, Rogers–Ramanujan identity, Rogers–Szegő polynomials
Stieltjes polynomial, Stieltjes–Wigert polynomials
Tricomi–Carlitz polynomial