q-Charlier polynomials

In mathematics, the q-Charlier polynomials^[1] 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 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

↑ There are similar named polynomials named alternative q-Charlier polynomials $K_{n} (x; a; q)$ which is another name for q-Bessel polynomials.

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[1] There are similar named polynomials named alternative q-Charlier polynomials $K_{n} (x; a; q)$ which is another name for q-Bessel polynomials.

[1]

q-Charlier polynomials

Definition

References

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