A family of log-gamma integrals and associated results

The authors present a systematic investigation of the following log-gamma integral: ∫0zlogΓ(t+1)dt and of its several related integral formulas. Relevant connections among the various mathematical constants involved naturally in the evaluation of the proposed integral are pointed out. Some approximate numerical values of the derivative ζ′(−1,a) of the Hurwitz zeta function are also considered. Importance of such derivatives as ζ′(−1,a) lies in their usefulness in the effective Lagrangian theory of quark confinement.