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On the multi-index (3m-parametric) Mittag-Leffler functions, fractional calculus relations and series convergence

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Central European Journal of Physics

Abstract

In this paper we consider a family of 3m-indices generalizations of the classical Mittag-Leffler function, called multi-index (3m-parametric) Mittag-Leffler functions. We survey the basic properties of these entire functions, find their order and type, and new representations by means of Mellin-Barnes type contour integrals, Wright p Ψ q -functions and Fox H-functions, asymptotic estimates. Formulas for integer and fractional order integration and differentiations are found, and these are extended also for the operators of the generalized fractional calculus (multiple Erdélyi-Kober operators). Some interesting particular cases of the multi-index Mittag-Leffler functions are discussed. The convergence of series of such type functions in the complex plane is considered, and analogues of the Cauchy-Hadamard, Abel, Tauber and Littlewood theorems are provided.

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8 ”Kliment Ohridski” bul., 1000, Sofia, Bulgaria

    Jordanka Paneva-Konovska

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, ”Acad. G. Bontchev” Street, Block 8, 1113, Sofia, Bulgaria

    Jordanka Paneva-Konovska

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  1. Jordanka Paneva-Konovska
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Correspondence to Jordanka Paneva-Konovska.

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Paneva-Konovska, J. On the multi-index (3m-parametric) Mittag-Leffler functions, fractional calculus relations and series convergence. centr.eur.j.phys. 11, 1164–1177 (2013). https://doi.org/10.2478/s11534-013-0263-8

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  • DOI: https://doi.org/10.2478/s11534-013-0263-8

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