An integral involving the generalized zeta function. (1990) - Elizalde, E.; Romeo, A.
Abstract : A general value for∫ a b d t log Γ ( t ), fora, b positive reals, is derived in terms of the Hurwitzζ function. That expression is checked for a previously known special integral, and the case wherea is a positive integer andb is half an odd integer is considered. The result finds application in calculating the numerical value of the derivative of the Riemann zeta function at the point− 1, a quantity that arises in the evaluation of determinants of Laplacians on compact Riemann surfaces.