Big q-Laguerre polynomials

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In mathematics, the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.


The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by


Recurrence and difference relations[edit]

Rodrigues formula[edit]

Generating function[edit]

Relation to other polynomials[edit]

Big q-Laguerre polynomials→Laguerre polynomials