Continuous Hahn polynomials

In mathematics, the continuous 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 
 give a detailed list of their properties.
Closely related polynomials include the dual Hahn polynomials "R""n"("x";γ,δ,"N"), the Hahn polynomials "Q""n"("x";"a","b","c"), and the continuous dual Hahn polynomials "S""n"("x";"a","b","c"). 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.
Orthogonality.
The continuous Hahn polynomials "p""n"("x";"a","b","c","d") are orthogonal with respect to the weight function
In particular, they satisfy the orthogonality relation
for formula_4, formula_5, formula_6, formula_7, formula_8, formula_9.
Recurrence and difference relations.
The sequence of continuous Hahn polynomials satisfies the recurrence relation
Rodrigues formula.
The continuous Hahn polynomials are given by the Rodrigues-like formula
Generating functions.
The continuous Hahn polynomials have the following generating function:
A second, distinct generating function is given by