An L-function extension of Ramanujan's formula for the Riemann zeta function with an entire parameter

Abstract. A famous formula of Ramanujan for the Riemann zeta function evaluated at odd integers is a special case of a much more general formula of Ramanujan in which an entire function satisfying certain growth and non-vanishing conditions appears. A proof of this formula using contour integration is given by Bruce Berndt in Part IV of the notebooks. Here we sketch an alternative proof and show how the formula may be extended to derive an analogous formula for Dirichlet L-functions.