An Extended k-type Hypergeometric Functions

arXiv: Classical Analysis and ODEs(2017)

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Abstract
Hypergeometric functions and their generalizations play an important r^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing (presumably new) extended $k-$type hypergeometric function $_{2}f_{1}^{k}[a, b; c; omega; z]$ and study various properties including integral representations, differential formulas and fractional integral and derivative formula.
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