# Some New Applications of Matrix Inversions in *A*_{r}

Article

DOI: 10.1023/A:1009809424076

- Cite this article as:
- Schlosser, M. The Ramanujan Journal (1999) 3: 405. doi:10.1023/A:1009809424076

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## Abstract

We apply multidimensional matrix inversions to multiple basic hypergeometric summation theorems to derive several multiple (q-)series identities which themselves do not belong to the hierarchy of (basic) hypergeometric series. Among these are A terminating and nonterminating q-Abel and q-Rothe summations. Furthermore, we derive some identities of another type which appear to be new already in the one-dimensional case.

multidimensional matrix inversionsmultiple q-series associated to the root systems A and DU(n + 1) seriesterminating and nonterminating A q-Abel summationsterminating and nonterminating A q-Rothe summations

## Copyright information

© Kluwer Academic Publishers 1999