Ramanujan\u27s Formula for the Riemann Zeta Function Extended to L-Functions

Ramanujan\u27s formula for the Riemann-zeta function is one of his most celebrated. Beginning with M. Lerch in 1900, there have been many mathematicians who have worked with this formula. Many proofs of this formula have been given over the last 100 years utilizing many techniques and extending the formula. This thesis provides a proof of this formula by the Mittag-Leffler partial fraction expansion technique. In comparison to the most recent proof by utilizing contour integration, the proof in this thesis is based on a more natural growth hypothesis. In addition to a less artificial approach, the partial fraction expansion technique used in this thesis yields a stronger convergence result. In addition to providing a new proof of this formula, the work in this thesis extends this formula to a series acceleration formula for Dirichlet L-series with periodic coefficients. The result is a. generalized character analog, which can be reduced to the original formula