On some Definite Integrals involving the Hurwitz Zeta function

TL;DR

This paper derives new integral formulas involving the Hurwitz zeta function and applies them to evaluate integrals of Bernoulli polynomials, log Gamma(q), and log sin(q).

Contribution

It introduces novel integral formulas with the Hurwitz zeta function and demonstrates their applications to classical special functions.

Findings

Derived new integral formulas involving the Hurwitz zeta function

Evaluated integrals of Bernoulli polynomials using these formulas

Connected the results to log Gamma(q) and log sin(q) integrals

Abstract

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Gamma(q) and log sin(q).