Partial Theta Functions. I. Beyond the Lost Notebook

By S. Ole Warnaar. 2001

123 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/b27969970b7f90b863ee19ffbe729ca598475745

Citations in the corpus

• HARDY-PETROVITCH-HUTCHINSON'S PROBLEM AND PARTIAL THETA FUNCTION (2011, unknown): “Since k = 3, 4, . . . , n is an arbitrary index, we get from (6) the following system of inequalities (7) δkδk−1 − 4δk−1 + 3 ≥ 0, k = 3, 4, . . . , n.”