  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.
