The Ramanujan Journal

, Volume 1, Issue 3, pp 243-274

First online:

Multidimensional Matrix Inversions and Ar and Dr Basic Hypergeometric Series

  • Michael SchlosserAffiliated withInstitut für Mathematik der Universität Wien

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We compute the inverse of a specific infinite r-dimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an r-dimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of another infinite r-dimensional matrix. As applications of our matrix inversions, we derive new summation formulas for multidimensional basic hypergeometric series.

multidimensional matrix inversions Ar basic hypergeometric series Dr basic hypergeometric series