TRUNCATED BILATERAL HYPERGEOMETRIC SERIES ASSOCIATED WITH NEGATIVE UNIT ARGUMENT

Abstract

In this paper we obtain some summation theorems for truncated bilateral generalized hypergeometric series involving negative unit argument given by

, ,
,
and
using series iteration techniques; where and are the functions of parameters Applying Rainville's limit formula for certain infinite products, some non terminating bilateral hypergeometric summation theorems with negative unit argument are also deduced, in terms of Gamma functions subject to certain conditions. The results presented here are presumably new.

Keywords and Phrases: Pochhammer Symbol; Gamma function; Rainville's limit formula; Unilateral and bilateral series; Truncated and non terminating series.

2010 AMS Subject Classifications: 33-Special Functions, Primary 33C99; Secondary 33C20.