PERIPHERY BEHAVIOUR OF SERIES IN
MITTAG-LEFFLER TYPE FUNCTIONS, I
Abstract. This is a survey on part of author's recent results on the subject. Different families of the the Mittag-Leffler functions and their 3-parametric generalizations are considered. First, asymptotic formulae necessary for proving the main results, are provided. Series defined by means of these families are further studied. Starting with their domains of convergence, the behaviour of such series on the peripheries of their convergence domains is investigated and analogues of the classical results for the power series are proposed.
AMS Subject Classification: 30B30, 31A20, 30B10, 40A30


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DOI: 10.12732/ijam.v29i1.6

Volume: 29
Issue: 1
Year: 2016