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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Schlosser, M. Multidimensional Matrix Inversions and Ar and Dr Basic Hypergeometric Series. The Ramanujan Journal 1, 243–274 (1997). https://doi.org/10.1023/A:1009705129155
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DOI: https://doi.org/10.1023/A:1009705129155