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Q Charlier polynomials

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In mathematics, the q-Charlier 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.

Definition

The q-Charlier polynomials are given in terms of the basic hypergeometric function by

c n ( q − x ; a ; q ) = 2 ϕ 1 ( q − n , q − x ; 0 ; q , − q n + 1 / a )

References

Q-Charlier polynomials Wikipedia
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