Q Laguerre polynomials - Alchetron, The Free Social Encyclopedia

In mathematics, the q-Laguerre polynomials, or generalized Stieltjes–Wigert polynomials P(α)
n(x;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme introduced by Daniel S. Moak (1981). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Definition

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

L n ( α ) ( x ; q ) = ( q α + 1 ; q ) n ( q ; q ) n 1 ϕ 1 ( q − n ; q α + 1 ; q , − q n + α + 1 x )

References

Q-Laguerre polynomials Wikipedia

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