Generalized the special hyper geometric Gp,n,r function's of the uniform integral

Abstract

Two new unified integral formulas involving a generalized Gp,n,r function are presented in this study. As corollaries, a few intriguing exceptional situations of the major findings are also taken into consideration. The Gp,n,r function's general nature allows for the specialization of the parameters in the given formulas to yield a number of results involving various special functions, including the exponential function, the Gp,n,r function, the Lommel function, the Struve function, the Wright generalized Bessel function, the Bessel function, and the generalized hyper geometric Gp,n,r function. There is also a detailed discussion of further results.