Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
Hjalmar Rosengren, Michael J. Schlosser, Universität Wien, Austria · Symmetry Integrability and Geometry Methods and Applications · 2020
Multidimensional matrix inversions provide 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 A r elliptic Jackson summation, as well as several quadratic, cubic and quartic summation formulas.