Certain classes of infinite sums evaluated by means of fractional calculus operators. (Q1394471)

The authors give alternative directs proofs of two of the main results of \textit{K. Nishimoto}, \textit{D.-K. Chyan}, \textit{S.-D. Lin} and \textit{S.-T. Tu} [J. Fractional Calc. 20, 91--97 (2001; Zbl 1004.26004)]. The paper also mentions the generalizations of the aforementioned results of Nishimoto et al. given earlier by \textit{S. Salinas de Romero} and \textit{H. M. Srivastava} [EAMJ, East Asian Math. J. 17, 135--146 (2001; Zbl 1007.26002)]. The authors further investigate some general classes of infinite sums (without using fractional calculus), which provide extensions to several recently established results on the subject of infinite sums.