Geodesic
Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems
Fractional calculus and applied analysis, Tome 13 (2010) no. 4, pp. 403-414

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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 large" values of indices that are used in the proofs of the convergence theorems for the considered series.
Keywords: Mittag-Leffler Functions, Inequalities, Asymptotic Formula, Cauchy-Hadamard, Summation of Divergent Series, Abel, Tauber and Littlewood Type Theorems 
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     author = {Paneva-Konovska, Jordanka},
     title = {Series in {Mittag-Leffler} {Functions:} {Inequalities} and {Convergent} {Theorems}},
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Paneva-Konovska, Jordanka. Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems. Fractional calculus and applied analysis, Tome 13 (2010) no. 4, pp. 403-414. http://geodesic.mathdoc.fr/item/FCAA_2010_13_4_a5/