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Generalized Lambert series identities

Published online by Cambridge University Press:  19 October 2005

Song Heng Chan
Song Heng Chan
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA, E-mail: songchan@math.uiuc.edu Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore
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Abstract

We present two infinite families of generalized Lambert series identities, and deduce several known identities from them. They include an identity due to M. Jackson, a corollary of Ramanujan's $_1\psi_1$-summation formula, and a recent identity of G. E. Andrews, R. P. Lewis and Z.-G. Liu.

Keywords

generalized Lambert seriesLambert seriesq-seriessums of squares33D1511D85
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 91 , Issue 3 , November 2005 , pp. 598 - 622
Copyright
2005 London Mathematical Society

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