An Infinite Integral of Three Constants: Boros Integral for Polynomial Families and Incomplete W-Functions

Abstract

In this paper, we explore the Boros integral with three parameters, which encompasses the incomplete W-functions and the Srivastava polynomial, a general class of polynomials. Our primary contribution is the derivation of the Boros integral for the product of a family of polynomials and the incomplete W-function. Furthermore, we present a novel family of special functions associated with the W-function, derived as a main result of our investigation. To expand the scope of our findings, we propose that the derived formulas can be generalized to incorporate classes of multivariable polynomials, thus opening the door for further exploration in the realm of special functions.