An introduction to the Barnes double gamma function with an application to an integral involving the cotangent function

Abstract

We show a direct approach to Kinkelin's integral involving the cotangent function.

This includes a new Proposition 7.3 involving the integral of the second derivative of the Hurwitz zeta function

References in corpus (3)

• Contributions to the Theory of the Barnes Function
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Some applications of the Dirichlet integrals to the summation of series and the evaluation of integrals involving the Riemann zeta function