Generating functions for a class of q-polynomials
Date
2009-09-04T18:33:38Z
Authors
Srivastava, H.M.
Agarwal, A. K.
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Some simple ideas are used here to prove a theorem on generating functions for a certain class of q-polynomials. This general theorem is then applied to derive a fairly large number of known as well as new generating functions for the familiar q-analogues of various polynomial systems including, for example, the classical orthogonal polynomials of Hermite, Jacobi, and Laguerre. A number of other interesting consequences of the theorem are also discussed.
Description
Keywords
generating functions, q-polynomials, classical orthogonal polynomials, q-series, hypergeometric identities, quadratic transformations, special functions, q-Pfaff transformation, Kummer's summation theorem, Gauss's second theorem, Pfaff-Saalschutz theorem, basic (or q-) hypergeometric function, Gaussian polynomial (or q-binomial coefficient), q-binomial theorem, q-Laguerre polynomials, little q-Jacobi polynomials, q-Hahn polynomials, q-Meixner polynomials, q-Charlier polynomials, Heine's transformation, confluent hypergeometric function, q-Hermite polynomials, q-summation formula, q-hypergeometric polynomials