Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• ISSN: 1815-0659
• Main Authors: Rosengren, Hjalmar, Schlosser, Michael J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210760
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems. Hjalmar Rosengren and Michael J. Schlosser/ SIGMA 16 (2020), 088, 21 pages

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 ᵣ elliptic Jackson summation, as well...