Convergence of series in three parametric Mittag-Leffler functions. (English) Zbl 1324.33015
Summary: In this paper we consider a family of \(3\)-index generalizations of the classical Mittag-Leffler functions. We study the convergence of series in such functions in the complex plane. First we find the domains of convergence of such series and then study their behaviour on the boundaries of these domains. More precisely, Cauchy-Hadamard, Abel, Tauber and Littlewood type theorems are proved as analogues of the classical theorems for the power series.
MSC:
| 33E12 | Mittag-Leffler functions and generalizations |
| 40E05 | Tauberian theorems |
| 40A30 | Convergence and divergence of series and sequences of functions |
Keywords:
Mittag-Leffler function and its generalizations; series in special functions in complex domain; Cauchy-Hadamard; Abel-type theorem; Tauber-type theorem; Littlewood-type theorems; entire functions; summation of divergentReferences:
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