Certain classes of finite-series relationships and generating functions involving the generalized Bessel polynomials

摘要

Recently, by making use of the familiar group-theoretic (Lie algebraic) method, a certain mixed trilateral finite-series relationship was proven for the generalized Bessel polynomials. The main object of this paper is to derive several substantially more general families of bilinear, bilateral, and mixed multilateral finite-series relationships and generating functions for these and other related classes of hypergeometric polynomials. A duly corrected and modified analogue of the aforementioned trilateral finite-series relationship is shown to follow by suitably specializing one of the general results presented here. Several closely related (presumably new) finite-series relationships and generating functions, some of which also involve (for example) the Stirling numbers of the second kind, are onsidered rather briefly.