Communications of the
Korean Mathematical Society CKMS

Motivated essentially by Brychkov's work \cite{Bryc}, we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov\cite{Bryc}, Choi and Rathie \cite{Ch-Ra-15}), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

Keywords: Gamma function, Psi and polygamma functions, Hurwitz zeta function, hypergeometric function, generalized hypergeometric function, classical summation theorems

MSC numbers: Primary 33B20, 33C20; Secondary 33B15, 33C05