International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 630458, 21 pages
doi:10.1155/2010/630458
Research Article

A Rademacher Type Formula for Partitions and Overpartitions

Andrew V. Sills

Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460-8093, USA

Received 3 July 2009; Revised 21 January 2010; Accepted 28 February 2010

Academic Editor: Stéphane Louboutin

Copyright © 2010 Andrew V. Sills. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Rademacher-type convergent series formula which generalizes the Hardy-Ramanujan-Rademacher formula for the number of partitions of n and the Zuckerman formula for the Fourier coefficients of ϑ4(0∣τ)-1 is presented.