Evaluation of a class of2F1(-1) series - Zheng, De-Yin (Utilitas Mathematica, 2011)
The well-known Kummer's summation formula evaluates the well-poised series 2F1 (-1). For the non-well-poised series 2F1(a,b;c;-1), Vidünas has considered its evaluations in the case when c - a + b is an integer. In this paper, we deal first with one-parameter general nonterminating 2F1(-1) of evaluations. With Whipple's transformation and Dixon, Watson, Whipple formula, we get the sixteen summation formulas in this type series, among which one formula was essentially known to Vidünas in 2000's and the four formulas were essentially known to Maier in 2006's. Then by means of these nonterminating formulas, the eleven terminating 2F1(-1) summation formulas are established by using the limit truncation methods, included two formulas due to EKHAD through computer programs.