  Series acceleration formulas are obtained for Dirichlet series with periodic
coefficients. Special cases include Ramanujan's formula for the values of the
Riemann zeta function at the odd positive integers exceeding two, and related
formulas for values of Dirichlet L-series and the Lerch zeta function. Such
formulas have been made famous by Lerch, Ramanujan, Grosswald, Berndt, and
others. The approach herein is based on the partial fraction expansion of the
hyperbolic cotangent, and as such is somewhat more elementary than previous
approaches, yet is quite general.
