A class of hypergeometric polynomials

Abstract

The object of the present paper is first to derive an interesting unification (and generalization) of a fairly large number of finite summation formulas including, for example, those that appeared in this Journal recently. We then briefly remark on its various (known or new) special cases which are associated with certain classes of hypergeometric polynomials in one and two variables. We also give several further generalizations (involving multiple series with essentially arbitrary terms) which are shown to be applicable in the derivation of analogous summation formulas for hypergeometric series (and polynomials) in three and more variables. Finally, with a view to presenting relevance of these types of results in various seemingly diverse areas of applied sciences and engineering, some indication of applicability is provided.

Reduction formulas associated with series involving arbitrary coefficients

“…Reduction formulas (or summation theorems) concerning different classes of special functions are invariably used in various problems of theoretical physics, applied mathematics and engineering sciences (see, for example [3], [6], [14], [15] and [l6]).…”