\(q\)-generating functions for one and two variables. (English) Zbl 1132.33335

Ernst, Thomas

Bull. Belg. Math. Soc. - Simon Stevin 12, No. 4, 589-605 (2005).

Summary: We use a multidimensional extension of Bailey’s transform to derive two very general \(q\)-generating functions, which are \(q\)-analogues of a paper by H. Exton [Ark. Mat. 30, No. 2, 245–258 (1992; Zbl 0785.33009)]. These expressions are then specialized to give more practical formulae, which are \(q\)-analogues of generating relations for Karlssons generalized Kampé de Fériet function. A number of examples are given including \(q\)-Laguerre polynomials of two variables.

MSC:

33D70	Other basic hypergeometric functions and integrals in several variables
33C65	Appell, Horn and Lauricella functions
05A30	\(q\)-calculus and related topics

Citations:

Zbl 0785.33009