Evaluation of Log-tangent Integrals by series involving $\zeta(2n+1)$

Abstract

In this note, we show that the values of integrals of the log-tangent function with respect to any square-integrable function on $\left[0 , \frac{\pi}{2} \right]$ may be determined by a finite or infinite sum involving the Riemann Zeta-function at odd positive integers.