q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS {Ln(-N)(·q)}n=0 FOR POSITIVE INTEGERS N

Title & Authors
q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS {Ln(-N)(·q)}n=0 FOR POSITIVE INTEGERS N
Moreno, Samuel G.; Garcia-Caballe, Esther M.;

Abstract
The family of q-Laguerre polynomials $\small{\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}}$ is usually defined for 0 < q < 1 and $\small{{\alpha}}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter $\small{{\alpha}}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter $\small{{\alpha}}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\small{\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}}$, for positive integers N, become orthogonal.
Keywords
non-standard orthogonality;q-Laguerre polynomials;basic hypergeometric series;
Language
English
Cited by
1.
Weighted enumerations of boxed plane partitions and the inhomogeneous five-vertex model, Journal of Mathematical Sciences, 2013, 192, 1, 70
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