Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions

Abstract The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized Erdélyi-Kober fractional differential and integral operators is demonstrated and discussed. View Full-Tex