Partial Theta Functions. I. Beyond the Lost Notebook

Warnaar, S. O. (2003) Partial Theta Functions. I. Beyond the Lost Notebook. Proceedings of the London Mathematical Society, 87 2: 363-395. doi:10.1112/S002461150201403X

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Author Warnaar, S. O.
Title Partial Theta Functions. I. Beyond the Lost Notebook
Journal name Proceedings of the London Mathematical Society   Check publisher's open access policy
ISSN 1460-244X
0024-6115
Publication date 2003-09-01
Year available 2003
Sub-type Article (original research)
DOI 10.1112/S002461150201403X
Open Access Status Not yet assessed
Volume 87
Issue 2
Start page 363
End page 395
Total pages 33
Place of publication London, England
Publisher London Mathematical Society
Language eng
Subject 0102 Applied Mathematics
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.
Formatted 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. 2000 Mathematics Subject Classification 05A30, 33D15, 33D90.
Keyword the lost notebook
partial theta functions
Rogers–Ramanujan identities
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
 
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Created: Thu, 03 Dec 2009, 22:16:10 EST