Orders and types of the Wright and Mittag-Leffler functions. (Russian. English summary) Zbl 1459.30001
Summary: 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.
MSC:
| 30D20 | Entire functions of one complex variable (general theory) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 33E12 | Mittag-Leffler functions and generalizations |
References:
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