Little q-Laguerre polynomials

In mathematics, the little q-Laguerre polynomials p_n(x;a|q) or Wall polynomials W_n(x; b,q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme closely related to a continued fraction studied by Template:Harvs. (The term "Wall polynomial" is also used for an unrelated Wall polynomial in the theory of classical groups.) Template:Harvs give a detailed list of their properties.

Definition

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

$p_n(x;a|q)={}_2{\varphi }_1(q^{-n},0;aq;q,qx)=\frac{1}{(a^{-1}{q}^{-n};q{)}_n}{}_2{\varphi }_0(q^{-n},x^{-1};;q,x/a)$

See also

[1]

References

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