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Expansions for (q)∞n2+2n and basic hypergeometric series in U(n)

By Verne E. Leininger and Stephen C. Milne

Abstract

AbstractIn this paper we derive new, more symmetrical expansions for (q; q)∞n2+2n by means of our multivariable generalization of Andrews' variation of the standard proof of Jacobi's (q; q)∞3 result. Our proof relies upon a new multivariable extension of the Jacobi triple product identity. This result is deduced elsewhere by the second author from a U(n) multiple basic hypergeometric series generalization of Watson's very-well-poised 8φ7 transformation. The derivation of our (q; q)∞n2+2n result utilizes partial derivatives and dihedral group symmetries to write the sum over regions in n-space. In addition, we prove that our expansions for (q; q)∞n2+2n are equivalent to Macdonald's An family of eta-function identities

Publisher: Published by Elsevier B.V.
Year: 1999
DOI identifier: 10.1016/S0012-365X(98)00375-6
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