Some families of infinite series summable by means of fractional calculus

In a Five-volume work published recently, K. Nishimoto [1] has presented a systematic account of the theory and applications of fractional calculus in a number of areas (such as ordinary and partial differential equations, special functions. and summation of series). In 2001, K. Nishimoto, D.-K. Chyan, S.-D. Lin and S.-T. Tu [11] derived the following interesting families of infinite series via fractional calculus, Sigma(k=2)(infinity) (-c)k/k(k - 1) (kz - c)/(z - c)(k-1) = c(2) (/-c/z - c/ < 1). The object of the present paper is to extend the above families of infinite series to more general closed form relations. Various numerical results are also provided.