Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function

Abstract

This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving fundamental constants. The goal of this paper is to expand upon current tables of definite integrals with the aim of assisting researchers in need of new integral formulae.

Keywords

• Bose–Einstein
• definite integral
• Lerch function
• Catalan’s constant
• Glaisher’s constant
• contour integral