A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series

Details A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series

2000-10-16

arxiv.org/abs/math/0010162v1

Mathematics

Classical Analysis and ODEs

LaTeX2e, 26 pages, submitted to Rocky Mount. J. Math., spec. vol., conference proceedings of SF2000, Tempe, Arizona, May 29 -

Scientific paper

In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of Ramanujan's 1-psi-1 summation theorem. From this new A_n 1-psi-1 summation and from an A_n 1-psi-1 summation of Gustafson we deduce two lemmas for deriving simple A_n generalizations of bilateral basic hypergeometric series identities. These lemmas are closely related to the Macdonald identities for A_n. As samples for possible applications of these lemmas, we provide several A_n extensions of Bailey's 2-psi-2 transformations, and several A_n extensions of a particular 2-psi-2 summation.

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