PERIPHERY BEHAVIOUR OF SERIES IN
MITTAG-LEFFLER TYPE FUNCTIONS, II
Jordanka Paneva-Konovska1,2
1 Faculty of Applied Mathematics and Informatics
Technical University of Sofia
8 Kliment Ohridski, Sofia - 1000, BULGARIA
2 Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
`Acad. G. Bontchev' Street, Block 8, Sofia - 1113
Abstract. This is a survey on a part of author's recent results on the subject. It is devoted to different systems of the Mittag-Leffler functions and their 3-parametric generalizations. First, asymptotic formulae necessary for obtaining the main results, are provided. Series defined by means of these systems are further studied. Starting with their domains of convergence, the behaviours of such series on the peripheries of their convergence domains are investigated and analogues of the classical results for the power series are proposed.

This serves as Part II, of our previous paper [16].

AMS Subject Classification: 30B30, 30B40, 31A20, 30B10, 40A30
Key Words and Phrases: power series, series in special functions, Mittag-Leffler functions and generalizations, convergence, uniform convergence, Hadamard gaps, overconvergence


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DOI: 10.12732/ijam.v29i2.2

Volume: 29
Issue: 2
Year: 2016