A family of hyper-Bessel functions and convergent series in them

被引：0
作者：
Jordanka Paneva-Konovska
机构：
[1] Technical University of Sofia,Faculty of Applied Mathematics and Informatics
[2] Bulgarian Academy of Sciences,Institute of Mathematics and Informatics
来源：
Fractional Calculus and Applied Analysis | 2014年 / 17卷
关键词：
hyper-Bessel function; hyper-Bessel differential operator; series in hyper-Bessel functions; convergence of series in a complex plane; Primary 40A30, 30D15; Secondary 33E12, 31A20, 30A10;
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摘要：
The Delerue hyper-Bessel functions that appeared as a multi-index generalizations of the Bessel function of the first type, are closely related to the hyper-Bessel differential operators of arbitrary order, introduced by Dimovski. In this work we consider an enumerable family of hyper-Bessel functions and study the convergence of series in such a kind of functions. The obtained results are analogues to the ones in the classical theory of the widely used power series, like Cauchy-Hadamard, Abel and Fatou theorem.
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页码：1001 / 1015
页数：14
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