On some subclasses of hypergeometric functions with Djrbashian Cauchy type kernel

Volume 10, Issue 5, pp 2340--2349 http://dx.doi.org/10.22436/jnsa.010.05.06

Publication Date: May 22, 2017 Submission Date: March 24, 2017

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Authors

Joel Esteban Restrepo - Institute of Mathematics, University of Antioquia, Cl. 53 - 108, Medellin, Colombia. Armen Jerbashian - Institute of Mathematics, University of Antioquia, Cl. 53 - 108, Medellin, Colombia. Praveen Agarwal - Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India.

Abstract

In this paper, some new integral representations are proved for several weighted hypergeometric functions introduced recently in [J. E. Restrepo, A. Kılıc¸man, P. Agarwal, O. Altun, Adv. Difference Equ., 2017 (2017), 11 pages]. Besides, some new subclasses of weighted hypergeometric functions containing the Djrbashian Cauchy type kernel are introduced. The series representing the considered hypergeometric functions are convergent out of some sets of zero !-capacity, and these hypergeometric functions have finite boundary values everywhere on \(|z|=1\), out of zero \(\omega\)-capacity sets.

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Keywords

• Weighted hypergeometric function
• Djrbashian Cauchy type kernel
• \(\omega\)-capacity
• boundary behavior.

MSC

•  33C20
•  31A10
•  31A20

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