Multidimensional Matrix Inversions and A r and D r Basic Hypergeometric Series
نویسنده
چکیده
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.
منابع مشابه
Basic Hypergeometric Series
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 ...
متن کاملA new multidimensional matrix inverse with applications to multiple q-series
We compute the inverse of a speciic innnite r-dimensional matrix, extending a matrix inverse of Krattenthaler. Our inversion is diierent from the r-dimensional matrix inversion recently found by Schlosser but generalizes a multidimensional matrix inversion previously found by Chu. As applications of our matrix inversion we derive some multidimensional q-series identities. Among these are q-anal...
متن کاملNoncommutative Extensions of Ramanujan’s 1ψ1 Summation ∗
Using functional equations, we derive noncommutative extensions of Ramanujan's 1 ψ 1 summation. 1. Introduction. Hypergeometric series with noncommutative parameters and argument, in the special case involving square matrices, have been the subject of recent study, see e.g. the papers by Duval and Ovsienko [DO], Grünbaum [G], Tirao [T], and some of the references mentioned therein. Of course, t...
متن کاملMULTILATERAL INVERSION OF Ar, Cr AND Dr BASIC HYPERGEOMETRIC SERIES
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey’s very-well-poised 6ψ6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different ...
متن کاملMULTILATERAL TRANSFORMATIONS OF q-SERIES WITH QUOTIENTS OF PARAMETERS THAT ARE NONNEGATIVE INTEGER POWERS OF q
Abstract. We give multidimensional generalizations of several transformation formulae for basic hypergeometric series of a specific type. Most of the upper parameters of the series differ multiplicatively from corresponding lower parameters by a nonnegative integer power of the base q. In one dimension, formulae for such series have been found, in the q → 1 case, by B. M. Minton and P. W. Karls...
متن کامل