Certain integrals involving generalized Mittag-Leffler type functions

Abstract

Introduction/purpose: Certain integrals involving the generalized Mittag-Leffler function with different types of polynomials are established. Methods: The properties of the generalized Mittag-Leffler function are used in conjunction with different kinds of polynomials such as Jacobi, Legendre, and Hermite in order to evaluate their integrals. Results: Some integral formulae involving the Legendre function, the Bessel Maitland function and the generalized hypergeometric functions are derived. Conclusions: The results obtained here are general in nature and could be useful to establish further integral formulae involving other kinds of polynomials.