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AN IDENTITY RELATING A THETA FUNCTION TO A SUM OF LAMBERT SERIES

Published online by Cambridge University Press:  18 April 2001

GEORGE E. ANDREWS ,
RICHARD LEWIS  and
ZHI-GUO LIU
GEORGE E. ANDREWS
Affiliation:
Mathematics Department, Pennsylvania State University, 228 McAllister Building, University Park, PA 16802, USA; e-mail: andrews@math.psu.edu
RICHARD LEWIS
Affiliation:
School of Mathematical Sciences, The University of Sussex, Brighton BN1 9QH; e-mail: r.p.lewis@sussex.ac.uk
ZHI-GUO LIU
Affiliation:
Mathematics Department, Xinxiang Education College, Xinxiang, Henan 453000, P. R. China; e-mail: xxlzg@public.xxptt.ha.cn
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Abstract

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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 1 , January 2001 , pp. 25 - 31
Copyright
© The London Mathematical Society 2001

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