Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773748 | Journal of Approximation Theory | 2017 | 29 Pages |
Abstract
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and show that the extended representations can be interpreted as examples of regularizations of integrals containing Meijer's G function. Second, we give new applications of both, known and extended representations. These include: inverse factorial series expansion for the Gauss type function, new information about zeros of the Bessel and Kummer type functions, connection with radial positive definite functions and generalizations of Luke's inequalities for the Kummer and Gauss type functions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
D.B. Karp, J.L. López,