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)
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
Jacobi polynomial, Jacobi theta function
Macdonald polynomial, Macdonald–Kostka polynomial, Macdonald spherical function
Meixner polynomial, Meixner-Pollaczek polynomial
Painlevé function, Painlevé transcendents
Riccati–Bessel function
Rogers–Askey–Ismail polynomial, Rogers–Ramanujan identity, Rogers–Szegő polynomials
Stieltjes polynomial, Stieltjes–Wigert polynomials