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Continuous q-Laguerre polynomials
In mathematics, the continuous q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
Definition
The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by 。
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
References
- Roelof Koekoek, Peter Lesky, Rene Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p514, Springer
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