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Big q-Laguerre polynomials

In mathematics, the big 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(x;a,b;q)=\frac{1}{(b^{-1}q^{-n};q)_n}{}_2\phi_1\left(q^{-n},aqx^{-1};aq;q,\frac{x}{b}\right)

Relation to other polynomials

Big q-Laguerre polynomials→Laguerre polynomials

References

Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

orthogonal-polynomials q-analogs special-hypergeometric-functions

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