Multidimensional matrix inversions. (English) Zbl 0854.65022

Schlosser, Michael

Sémin. Lothar. Comb. 35, B35g, 24 p. (1995).

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 an application of our matrix inversion, we derive new multidimensional bibasic summation formulas.

Reviewer: M.Schlosser

MSC:

65F05

Direct numerical methods for linear systems and matrix inversion

Keywords:

infinite \(r\)-dimensional matrix; matrix inversions; multidimensional bibasic summation formulas