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Partial Theta Functions. I. Beyond the Lost Notebook
Author(s) -
Warnaar S. Ole
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s002461150201403x
Subject(s) - mathematics , ramanujan's sum , ramanujan theta function , theta function , lemma (botany) , connection (principal bundle) , generalization , identity (music) , pure mathematics , mathematics subject classification , ramanujan tau function , algebra over a field , type (biology) , product (mathematics) , combinatorics , mathematical analysis , geometry , ecology , physics , poaceae , acoustics , biology
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.