Michael Schlosser
Published 2006-07-05Version 1
By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived. By a polynomial argument this 8-phi-7 summation is transformed to another multivariable 8-phi-7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6-phi-5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey's very-well-poised 6-psi-6 summation formula.
Analytic continuation of eigenvalues of the Lamé operator
A summation formula for a ${}_3F_2(1)$ hypergeometric series
Another proof of Bailey's 6-psi-6 summation
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