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Balanced 3 φ 2 summation theorems for U(n) basic hypergeometric series. (English) Zbl 0886.33014
The Bailey transform is G. E. Andrews’ [Proc. Symp. Pure Math. Am. Math. Soc., Columbus, Ohio 1978, Proc. Symp. Pure Math. 34, 1-24 (1979; Zbl 0403.33002)] codification in terms of matrix inversions of a technique of W. N. Bailey for generating new Rogers-Ramanujan type identities. It can also be used to exhibit the equivalence of certain pairs of identities such as the summation formulæ for the terminating balanced 3 φ 2 and the very-well-poised 6 φ 5 . In this paper, the author moves all of this machinery up to the context of multiple basic hypergeometric series very-well-poised on U(n+1). It is then used to recreate much of the classical theory of basic hypergeometric series in the more general context of multiple series over U(n+1).

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