A note on some new series of special functions

摘要

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].