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• W2080765493 abstract "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 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." @default.
• W2080765493 created "2016-06-24" @default.
• W2080765493 creator A5042060658 @default.
• W2080765493 date "2013-01-01" @default.
• W2080765493 modified "2023-10-16" @default.
• W2080765493 title "On the multi-index (3m-parametric) Mittag-Leffler functions, fractional calculus relations and series convergence" @default.
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• W2080765493 doi "https://doi.org/10.2478/s11534-013-0263-8" @default.
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