Bateman polynomials

The Bateman–Pasternack polynomials are a generalization introduced by Pasternack (1939).

occurs on the right-hand side of this equation because the Bateman polynomials as defined here must be scaled by a factor

to make them remain real-valued for imaginary argument.

The orthogonality relation is simpler when expressed in terms of a modified set of polynomials defined by

, for which it becomes The sequence of Bateman polynomials satisfies the recurrence relation[3] The Bateman polynomials also have the generating function which is sometimes used to define them.