A Note on Wright-type Generalized q-hypergeometric Function

Abstract

In 2001, Virchenko et al. published a paper on a new generalization of Gauss hypergeometric function, namely Wright-type generalized hypergeometric function. Present work aims to define the q-analogue generalized hypergeometric function, which reduces to generalized hypegeometric function by letting q tends to one, and study some new properties. Convergence of the series defining generalized q-hypergeometric function and properties including certain differentiation formulae and integral representations have been deduced.

Keywords

• basic hypergeometric functions in one variable ${}_r \phi_s$
• q-gamma functions
• q-beta functions and integrals
• q-calculus and related topics