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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 $\sp m\sb{\mu}G\sb q\sp{(n)}(\gamma\sb 1,...,\gamma\sb n;\delta\sb 1,...,\delta\sb m)$ 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 $\sb 6\Phi\sb 5$ summation theorem.

MSC:
33D80Connections of basic hypergeometric functions with groups, algebras and related topics
33D15Basic hypergeometric functions of one variable, ${}_r\phi_s$
33C60Hypergeometric integrals and functions defined by them
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References:
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