A new symmetry related to SU(n) for clasical basic hypergeometric series (Q1071917)

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 \(^ m_{\mu}G_ q^{(n)}(\gamma_ 1,...,\gamma_ n;\delta_ 1,...,\delta_ m)\) 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 \(_ 6\Phi_ 5\) summation theorem.