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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 088, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.088 (Mi sigma1625) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

Hjalmar Rosengrenab, Michael J. Schlosserc

a Department of Mathematics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
b University of Gothenburg, SE-412 96 Göteborg, Sweden
c Fakultät für Mathematik der Universität Wien, Oskar Morgenstern-Platz 1, A-1090 Wien, Austria
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DOI: https://doi.org/10.3842/SIGMA.2020.088
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.
Keywords: elliptic hypergeometric series, hypergeometric series associated with root systems, multidimensional matrix inversion.
Funding agency Grant number
Austrian Science Fund P32305
S9607
Swedish Research Council
The first author was partially supported by the Swedish Science Research Council. The second author was partially supported by Austrian Science Fund grants S9607 and P32305.
Received: May 6, 2020; in final form August 28, 2020; Published online September 24, 2020
Bibliographic databases:
Document Type: Article
MSC: 33D67
Language: English
Citation: Hjalmar Rosengren, Michael J. Schlosser, “Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems”, SIGMA, 16 (2020), 088, 21 pp.
Citation in format AMSBIB
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\by Hjalmar~Rosengren, Michael~J.~Schlosser
\paper Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
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\totalpages 21
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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