Crandall’s computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet L-series

Abstract

This paper extends tools developed by Crandall (2012) [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet L-series and character polylogarithms.