Linearization coefficients for Boas–Buck polynomial sets

摘要

In this paper, we express explicitly the linearization coefficients related to three Boas–Buck polynomial sets using their corresponding generating functions. We apply the obtained results to many classes of polynomials including some generalized hypergeometric polynomials. The corresponding linearization coefficients will be expressed by means of terminating generalized Kampé de Fériet functions which, for some cases, can be reduced to hypergeometric functions or hypergeometric terms using, with this purpose, some known reduction formulae. We obtain some well-known results as particular cases as well as some new reduction formulae.