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Bulletin of the London Mathematical Society 2001 33(1):25-31; doi:10.1112/blms/33.1.25
© 2001 by London Mathematical Society
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© London Mathematical Society

An Identity Relating a Theta Function to a Sum of Lambert Series

George E. Andrews, Richard Lewis and Zhi-Guo Liu

Mathematics Department, Pennsylvania State University 228 McAllister Building, University Park, PA 16802, USA; e-mail: andrews{at}math.psu.edu
School of Mathematical Sciences, The University of Sussex Brighton BN1 9QH; e-mail: r.p.lewis{at}sussex.ac.uk
Mathematics Department, Xinxiang Education College Xinxiang, Henan 453000, P. R. China; e-mail: xxlzg{at}public.xxptt.ha.cn

Received 1 October 1999. Revision received 4 February 2000.

We derive an identity connecting a theta function and a sum of Lambert series. As a consequence of this identity, we deduce a number of results of Jacobi, Dirichlet, Lorenz, Ramanujan and Rademacher.


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