In mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by Bateman (). The Bateman–Pasternack polynomials are a generalization introduced by . Bateman polynomials are given by where Pn is a Legendre polynomial. generalized the Bateman polynomials to polynomials Fmn with showed that the polynomials Qn studied by , see Touchard polynomials, are the same as Bateman polynomials up to a change of variable: more precisely Bateman and Pasternack's polynomials are special cases of the symmetric continuous Hahn polynomials.