Sums of certain classes of series (Q2717132)

The reviewer [Elem. Math. 43, No. 2, 54-58 (1988; Zbl 0681.33003)] obtained a family of combinatorial series identities by means of Kummer's summation theorem for the hypergeometric series \(_2F_1(a,1- a;b;{1\over 2})\). The authors of the present sequel to the reviewer's work [loc. cit.] derive several contiguous versions of the aforementioned combinatorial series identities. It should be remarked here that \textit{A. P. Prudnikov}, \textit{Yu. A. Brychkov} and \textit{O. I. Marichev} [Integrals and Series (Supplementary Chapters), ``Nauka'', Moscow. 1986; English translation, Gordon and Breach, New York, 1988; especially see pp. 491-492] have already listed numerous contiguous-function versions of the Kummer summation theorem involving the hypergeometric series \(_2F_1(a,k-a;b; {1\over 2})\) of \(_2F_1(k-a, a;b;{1\over 2})\) for \(k=0,2, \dots,6\).