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Partial Theta Functions. I. Beyond the Lost Notebook

Published online by Cambridge University Press:  26 September 2003

S. Ole Warnaar
S. Ole Warnaar
Affiliation:
Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia. E-mail: warnaar@ms.unimelb.edu.au
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Abstract

It is shown how many of the partial theta function identities in Ramanujan's lost notebook can be generalized to infinite families of such identities. Key in our construction is the Bailey lemma and a new generalization of the Jacobi triple product identity. By computing residues around the poles of our identities we find a surprising connection between partial theta function identities and Garrett–Ismail–Stanton-type extensions of multisum Rogers–Ramanujan identities.

Keywords

the lost notebookpartial theta functionsRogers–Ramanujan identities05A3033D1533D90
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 2 , September 2003 , pp. 363 - 395
Copyright
2003 London Mathematical Society

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Footnotes

Work supported by the Australian Research Council.