Evaluation of some explicit summation formulae for truncated Gauss function and applications

Abstract

In this paper, some explicit expressions for truncated Gauss’ hypergeometric series ?F? with argument 2, when one numerator and one denominator parameters are negative integers such as ?F? [?m, a; ?2m + j; 2]m ; m > j and ?F? [?m, a; ?2m ? j; 2]m ; m, j ? N are obtained with the help of Whipple and Vidunas identities respectively. Further, we derive some results as applications of these summation theorems.