Linearization Coefficients for Some Basic Hypergeometric Polynomials

Abstract

In this paper, we give a simple and original method based on inverse relation to express explicitly the linearization coefficients for some general classes of basic hypergeometric polynomial set in terms of the basic Kampé de Fériet function. We use symbolic computation algorithms, namely, q -Multisum to find recurrence relations for the resulting linearization coefficients and qsum17 to solve some from the obtained recurrence relations. In some cases, the linearization coefficients are reduced to hypergeometric functions or hypergeometric terms.