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

S. C. Milne·M. Schlosser
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Abstract

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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BibTeXRIS

S. C. Milne, M. Schlosser. 2000-10-16. A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series. https://doi.org/10.1216/rmjm/1030539696

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