$q$-Generating functions for one and two variables
Ernst, Thomas
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 589-605 / Harvested from Project Euclid
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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 Exton. 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.
Publié le : 2005-12-14
Classification:  33D70,  33C65 
@article{1133793346,
     author = {Ernst, Thomas},
     title = {$q$-Generating functions for one and two variables},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 589-605},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1133793346}
}

Ernst, Thomas. $q$-Generating functions for one and two variables. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  589-605. http://gdmltest.u-ga.fr/item/1133793346/