Mittag-Leffler Functions Inequalities Asymptotic Formula Cauchy-Hadamard Summation of Divergent Series Abel, Tauber and Littlewood Type Theorems
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 13, No 4, (2010), 403p-414p
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.