Al-Salam–Chihara polynomials


In mathematics, the Al-Salam–Chihara polynomials Qn are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by. give a detailed list of the properties of Al-Salam–Chihara polynomials.

Definition

The Al-Salam–Chihara polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by
where x = cos.

Orthogonality

Recurrence and difference relations

Rodrigues formula

Generating function

Relation to other polynomials