Orders and types of the Wright and Mittag–Leffler functions

An entire function, with coefficients involving products and quotients of a finite number of gamma functions, is considered. The order and the type of such a function, known as the generalized Wright function, are evaluated. Applications are given to evaluate the orders and types of the generalized Mittag–Leffler functions will even and odd parameters and of the generalized hypergeometric function. Special cases involving in particular Wright, Mittag–Leffler and the confluent hypergeometric Kummer functions are presented.