SOME HYPERGEOMETRIC GENERATING FUNCTIONS MOTIVATED BY THE WORK OF BEDIENT AND RAINVILLE

Print ISSN: 0972-7752 | Online ISSN: 2582-0850

Abstract

In this article, some hypergeometric generating relations involving Kamp\'{e} de F\'{e}riet's double hypergeometric functions are derived by using series rearrangement technique, a reduction formula and Whipple's quadratic transformation. Some special cases involving Appell's functions of second, third kind, Rainville polynomial and two Bedient's polynomials, are also obtained.

Keywords and Phrases

Hypergeometric functions, Series rearrangement technique, Whipple's quadratic transformation, Bedient polynomials.

A.M.S. subject classification

33C20, 33C45, 05A15.

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