SOME FAMILIES OF GENERATING FUNCTIONS FOR THE q-KONHAUSER POLYNOMIALS

Abstract

The $q$-Konhauser polynomials, which were introduced and investigated in several recent works, are $q$-biorthogonal with respect to the weight function $x^{\alpha }\;e_{q}(-x)$ over the semi-infinite interval $(0,\infty )$. In the present paper, we derive various families of multilinear and multilateral generating functions for these $q$-Konhauser polynomials. We also briefly consider several special cases and consequences of the results presented in this paper.