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Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Paneva-Konovska, Jordanka — 2007

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20 The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the...

Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems

Paneva-Konovska, Jordanka — 2010

Fractional Calculus and Applied Analysis

MSC 2010: 30A10, 30B10, 30B30, 30B50, 30D15, 33E12 In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we prove Cauchy-Hadamard, Abel, Tauber and Littlewood type theorems. Asymptotic formulae are also provided for the Mittag-Leffler functions in the case of " values of indices that are used in the proofs of the convergence theorems for the considered...

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

Paneva-Konovska, Jordanka — 2012

Mathematica Balkanica New Series

MSC 2010: 33E12, 30A10, 30D15, 30E15 We consider some families of 3-index generalizations of the classical Mittag-Le²er functions and study the behaviour of these functions in domains of the complex plane. First, some inequalities in the complex plane and on its compact subsets are obtained. We also prove an asymptotic formula for the case of "large" values of the indices of these functions. Similar results have also been obtained by the author for the classical Bessel functions and...

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