Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

Abstract

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.

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Cited by in corpus (4)

• Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems
• An Elliptic Hypergeometric Function Approach to Branching Rules
• Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
• Gustafson-Rakha-Type Elliptic Hypergeometric Series