Continuous dual Hahn polynomials

In mathematics, the continuous dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by

:S_n(x^2;a,b,c)= {}_3F_2(-n,a+ix,a-ix;a+b,a+c;1).\

give a detailed list of their properties.

Closely related polynomials include the dual Hahn polynomials R**n(x;γ,δ,N), the continuous Hahn polynomials p**n(x,a,b, , ), and the Hahn polynomials. These polynomials all have q-analogs with an extra parameter q, such as the q-Hahn polynomials Q**n(x;α,β, N;q), and so on.