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 Rn, the Hahn polynomials Qn, and the continuous dual Hahn polynomials Sn. These polynomials all have q-analogs with an extra parameter q, such as the q-Hahn polynomials Qn, and so on.Orthogonality
The continuous Hahn polynomials pn are orthogonal with respect to the weight function
In particular, they satisfy the orthogonality relation
for,,,,,.Recurrence and difference relations
The sequence of continuous Hahn polynomials satisfies the recurrence relationRodrigues formula
The continuous Hahn polynomials are given by the Rodrigues-like formulaGenerating functions
The continuous Hahn polynomials have the following generating function:
A second, distinct generating function is given byRelation to other polynomials
