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A new symmetry related to SU(n) for clasical basic hypergeometric series. (English) Zbl 0586.33012
A direct proof is given of an elegant new contiguous relation for classical, well-poised basic hypergeometric series which preserves the well-poised condition. The proof involves elementary series manipulations and does not depend upon the ”transposition symmetry” of the general bisymmetric polynomials μ m G q (n) (γ 1 ,···,γ n ;δ 1 ,···,δ m ) which was used to establish the ordinary or '' q=1 '' case of the identity. The new contiguous relation can be considered as generalization of the 6 Φ 5 summation theorem.
33D80Connections of basic hypergeometric functions with groups, algebras and related topics
33D15Basic hypergeometric functions of one variable, r ϕ s
33C60Hypergeometric integrals and functions defined by them