This material has been published in Proc. Amer. Math. Soc. 124 (1996), 47-59, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the American Mathematical Society. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

A new matrix inverse

(13 pages)

Abstract. We compute the inverse of a specific infinite-dimensional matrix, thus unifying a number of previous matrix inversions. Our inversion theorem is applied to derive a number of summation formulas of hypergeometric type.

Comment: Michael Schlosser found a far-reaching generalization of the matrix inversion of this paper. He uses his generalization to derive many new summation formulas for Ar and Dr basic hypergeometric series identities. All this is subject of the paper "Multidimensional matrix inversions and Ar and Dr basic hypergeometric series", The Ramanujan J. 1 (1997), 243-274.

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