An integral involving the generalized zeta function

E. Elizalde and A. Romeo

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-8

Abstract:

A general value for ∫ a b d t log Γ ( t ) , for a , b positive reals, is derived in terms of the Hurwitz ζ function. That expression is checked for a previously known special integral, and the case where a is a positive integer and b 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.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:296127

DOI: 10.1155/S0161171290000679

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