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Journal

2013 | 11 | 10 | 1164-1177

Article title

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

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EN

Abstracts

EN
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 pΨq-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.

Publisher

Journal

Year

Volume

11

Issue

10

Pages

1164-1177

Physical description

Dates

published
1 - 10 - 2013
online
19 - 12 - 2013

References

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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0263-8
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