N-Fractional calculus of products of some power functions and some doubly infinite sums

摘要

In this article, the N-fractional calculus of the following products of power functions: ((z - c)(alpha) center dot (z - c)(beta))(gamma), (z - c)(beta) center dot (z - c)(alpha))(gamma), and ((z - c)(alpha+beta))(gamma) (z - c not equal 0) are discussed. Moreover, an application of the N-fractional calculus ((z - C) - (z - C)')(gamma) to the following doubly infinite sum: [GRAPHICS] where L(alpha,beta,gamma; m) :=Gamma(alpha+1)Gamma(gamma+1)(k - alpha+m)Gamma(gamma - beta - m)/k!center dot m Gamma(alpha - k+1)Gamma(k - alpha)Gamma(-beta) (alpha,beta,gamma is not an element of Z(0))(+) is reported. (C) 2006 Elsevier Inc. All rights reserved.