Some double-series identities and associated generating-function relationships

Abstract

The main object of the present work is to investigate several families of double-series identities and their applications to the Srivastava-Daoust hypergeometric function in two variables. A number of associated generating-function relationships, involving certain classes of hypergeometric polynomials, are also considered.

Certain cubic reduction formulas involving hypergeometric functions

“…Our present investigation is motivated essentially by the usefulness of several interesting and widespread developments of general double-series identities and reduction formulas for Srivastava-Daoust double hypergeometric functions (for example) Buschman-Srivastava[3, p.439], Srivastava [16] and [17], Chen-Srivastava [4], Chen-Liu-Srivastava [5], Olver et al [7], Prudnikovet al [8], two transformations (one product theorem of two 1 F 1 hypergeometric functions and another product theorem of two 0 F 2 hypergeometric functions) of Srinivasa Ramanujan [11, p.106, Q.N. (5) and Q.N.…”

Applications of Some Hypergeometric Summation Theorems Involving Double Series

“…The present investigation is motivated by the potential need for reduction formulas for hypergeometric functions in two and more variables (see, for details, [2], [3] and [4]; see also [8]). With this purpose in view, we make use of series rearrangement techniques, in conjunction with the above (known or easily derivable) hypergeometric summation theorems, in order to derive a number of general double series identities and hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function which is the case n = 2 of the definition (1.3) (see also [1]).…”