Multidimensional matrix inversions and Ar and Dr
basic hypergeometric series
(34 pages)
Abstract.
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.
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