Certain classes of series identities involving binomial coefficients
Motivated essentially by several series identities considered earlier by the reviewer [Elem. Math. 43, 54-58 (1988; Zbl 0619.33003)], the authors derive a total of nine similar results by employing various known contiguous-function analogues of the familiar Kummer summation theorem for the hypergeometric \(_2F_1(\frac 12)\) series. For various closely-related series identities, one may refer to the recent works of \textit{J. Choi}, \textit{P. Zörnig} and \textit{A. K. Rathie} [Commun. Korean Math. Soc. 14, No. 3, 641-647 (1999; Zbl 0974.33015)]. Basic (or \(q-)\) extensions of the aforementioned series identities were also investigated by the reviewer [Proc. Jap. Acad., Ser. A 65, No. 1, 8-11 (1989; Zbl 0653.33004)].
scientific article; zbMATH DE number 1733470