Continuous q-Laguerre polynomials

In mathematics, the continuous 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.

Definition

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by ]][1]

P_{n}^{(\alpha)}(x|q)=\frac{(q^\alpha+1;q)_{n}}{(q;q)_{n}}_{3}\Phi_{2}(q^{-n},q^{\alpha/2+1/4}e^{i\theta},q^{\alpha/2+1/4}*e^{-i\theta};q^{\alpha+1},0|q,q)

References

  1. Roelof Koekoek, Peter Lesky, Rene Swarttouw,Hypergeometric Orthogonal Polynomials and Their q-Analogues, p514, Springer
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