Certain unified integration formulas associated with generalized k-Bessel function

TL;DR

This paper develops generalized integration formulas involving the generalized k-Bessel function, leading to representations of Wright-type functions and exploring special cases to extend mathematical understanding.

Contribution

It introduces new generalized integration formulas with the k-Bessel function and derives related Wright-type function representations, expanding existing mathematical frameworks.

Findings

Derived new integration formulas involving the generalized k-Bessel function

Represented Wright-type functions using these formulas

Explored special cases to illustrate the formulas' versatility

Abstract

Our purpose in this present paper is to investigate generalized integration formulas containing the generalized $k$-Bessel function $W_{v,c}^{k}(z)$ to obtain the results in representation of Wright-type function. Also, we establish certain special cases of our main result.