A note on some new series of special functions

Abstract

Recently, Brychkov [On some new series of special functions. Appl Math Comput. 2007;187:101–104] obtained several finite and infinite series identities involving special functions by making use of an operator related to the Riemann–Liouville fractional calculus operator. In this paper, we present several identities involving the Jacobi polynomials, the generalized Laguerre function and the first Appell's function. These relations are obtained by using a fractional calculus operator related to the Riemann–Liouville operator and a new transformation formula [Tremblay R, Gaboury S, Fugère B-J. A new transformation formula for fractional derivatives with applications. Integral Transforms Spec Funct. 2013;24(3):172–186].