Michael J. Schlosser

A new multivariable 6Ψ6 summation formula

(16 pages)

Abstract. By multidimensional matrix inversion, combined with an Ar extension of Jackson's 8Φ7 summation formula by Milne, a new multivariable 8Φ7 summation is derived. By a polynomial argument this 8Φ7 summation is transformed to another multivariable 8Φ7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6Φ5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey's very-well-poised 6Ψ6 summation formula.

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