On some subclasses of hypergeometric functions with Djrbashian Cauchy type kernel

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 ω-capacity, and these hypergeometric functions have finite boundary values everywhere on │z│ = 1, out of zero ω-capacity sets.