Big q Laguerre polynomials - Alchetron, the free social encyclopedia

In mathematics, the big 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

P n ( x ; a , b ; q ) = 1 ( b − 1 ∗ q − n ; q , n ) ∗ 2 Φ 1 ( q − n , a q x − 1 ; a q | q ; x b )

Relation to other polynomials

Big q-Laguerre polynomials→Laguerre polynomials

References

Big q-Laguerre polynomials Wikipedia

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Contents

Definition

Relation to other polynomials

References