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

作者：Paneva Konovska Jordanka^*

来源：Fractional Calculus and Applied Analysis, 2014, 17(4): 1001-1015.

DOI：10.2478/s13540-014-0211-3

• hyper-Bessel function
• hyper-Bessel differential operator
• series in hyper-Bessel functions
• convergence of series in a complex plane

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.

• 出版日期2014-12