Bounds for Incomplete Confluent Fox–Wright Generalized Hypergeometric Functions

Abstract

We establish several new functional bounds and uniform bounds (with respect to the variable) for the lower incomplete generalized Fox–Wright functions by means of the representation formulae for the McKay Iν Bessel probability distribution’s cumulative distribution function. New cumulative distribution functions are generated and expressed in terms of lower incomplete Fox–Wright functions and/or generalized hypergeometric functions, whilst in the closing part of the article, related bounding inequalities are obtained for them.

Keywords

• modified Bessel functions of the first kind
• McKay’s \({I_\nu}\) Bessel distribution
• lower incomplete Fox–Wright functions
• cumulative distribution function
• functional bounding inequality