5 papers
Partial-sum analogues of the Rogers-Ramanujan identities
S. Ole Warnaar
A new type of polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product-side of the Rogers-Ramanujan identities is replaced by a partial theta sum and the…
The generalized Borwein conjecture. I. The Burge transform
S. Ole Warnaar
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) A…
A generalization of the q-Saalschutz sum and the Burge transform
A. Schilling, S. O. Warnaar
A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge…
Conjugate Bailey pairs
Anne Schilling, S. Ole Warnaar
In this paper it is shown that the one-dimensional configuration sums of the solvable lattice models of Andrews, Baxter and Forrester and the string functions associated with admis…
An A Bailey lemma and Rogers--Ramanujan-type identities
George E. Andrews, Anne Schilling, S. Ole Warnaar
Using new -functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A_2 version of the classical Bailey lemma. We apply our result, which is di…