Some definite logarithmic integrals from Euler sums, and other integration results

Mark W. Coffey
Department of Physics
Colorado School of Mines
Golden, CO 80401
December 28, 2009

Abstract
We present explicit expressions for multi-fold logarithmic integrals that are
equivalent to sums over polygamma functions at integer argument. Such rela-
tions find application in perturbative quantum field theory, quantum chemistry,
analytic number theory, and elsewhere. The analysis includes the use of prop-
erties of a variety of special functions.