Multidimensional matrix inversions and elliptic hypergeometric
series on root systems
Multidimensional matrix inversions is a powerful tool for studying
multiple hypergeometric series. In order to extend this technique to
elliptic hypergeometric series, we present three new multidimensional
matrix inversions. As applications, we obtain a new Ar
elliptic Jackson summation, as well as several quadratic, cubic and
quartic summation formulas.
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