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rogers–ramanujan identities

Proceedings of the London Mathematical Society (1)

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Partial Theta Functions. I. Beyond the Lost Notebook
S. Ole Warnaar
Journal:

Proceedings of the London Mathematical Society / Volume 87 / Issue 2 / September 2003

Published online by Cambridge University Press:

26 September 2003, pp. 363-395

Print publication:

September 2003
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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.