Hjalmar Rosengren and Michael J. Schlosser

Multidimensional matrix inversions and elliptic hypergeometric series on root systems

(21 pages)

Abstract. 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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