Fatou Type Theorems for Series in Mittag-Leffler Functions

被引：7

作者：

Paneva-Konovska, Jordanka ^{[1
]}

机构：

[1] Tech Univ Sofia, Fac Appl Math & Informat, Sofia 1000, Bulgaria

来源：

APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12) | 2012年 / 1497卷

关键词：

Mittag-Leffler functions; inequalities; asymptotic formula; Cauchy-Hadamard; Abel and Fatou type theorems; FRACTIONAL CALCULUS;

D O I：

10.1063/1.4766800

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.

引用

页码：318 / 325

页数：8

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