The generalized Borwein conjecture. I. The Burge transform

Details The generalized Borwein conjecture. I. The Burge transform The generalized Borwein conjecture. I. The Burge transform

2000-11-27

arxiv.org/abs/math/0011220v1

Contemp. Math. 291 (2001), 243--267

Mathematics

Combinatorics

25 pages, AMS-LaTeX

Scientific paper

Given an arbitrary ordered pair of coprime integers (a,b) we obtain a pair of identities of the Rogers--Ramanujan type. These identities have the same product side as the (first) Andrews--Gordon identity for modulus 2ab\pm 1, but an altogether different sum side, based on the representation of (a/b-1)^{\pm 1} as a continued fraction. Our proof, which relies on the Burge transform, first establishes a binary tree of polynomial identities. Each identity in this Burge tree settles a special case of Bressoud's generalized Borwein conjecture.

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