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Mathematica Slovaca

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Volume 64, Issue 1

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Convergence of series in three parametric Mittag-Leffler functions

Jordanka Paneva-Konovska
  • Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8, bul. Kliment Ohridski, BG-1000, Sofia, Bulgaria
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Published Online: 2014-03-06 | DOI: https://doi.org/10.2478/s12175-013-0188-0

Abstract

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: Primary 33E12, 40E05, 40A30; Secondary 30B30, 40G10

Keywords: Mittag-Leffler function and its generalizations; series in special functions in complex domain; Cauchy-Hadamard; Abel; Tauber and Littlewood type theorems; entire functions; summation of divergent series

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About the article

Published Online: 2014-03-06

Published in Print: 2014-02-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 1, Pages 73–84, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-013-0188-0.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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