Paneva-Konovska, Jordanka Series in Mittag-Leffler functions: inequalities and convergent theorems. (English) Zbl 1221.30006 Fract. Calc. Appl. Anal. 13, No. 4, 403-414 (2010). Summary: For series defined by means of Mittag-Leffler functions, on the boundary of their domain of convergence in the complex plane, we prove Cauchy-Hadamard, Abel, Tauber, and Littlewood type theorems. Asymptotic formulas 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. Cited in 4 Documents MSC: 30B10 Power series (including lacunary series) in one complex variable 30B30 Boundary behavior of power series in one complex variable; over-convergence Keywords:Mittag-Leffler functions; Cauchy-Hadamard type theorems; Abel type theorems; Tauber type theorems; Littlewood type theorems PDFBibTeX XMLCite \textit{J. Paneva-Konovska}, Fract. Calc. Appl. Anal. 13, No. 4, 403--414 (2010; Zbl 1221.30006) Full Text: EuDML