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A generalization of the q-Saalschutz sum and the Burge transform

A. Schilling·S. O. Warnaar
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Abstract

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 tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.

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A. Schilling, S. O. Warnaar. 1999-09-08. A generalization of the q-Saalschutz sum and the Burge transform. https://arxiv.org/abs/math/9909044

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