Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture

Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture

We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable,...

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Veröffentlicht in:arXiv.org 2009-05
Hauptverfasser: Langer, Robin, Schlosser, Michael J, Warnaar, S Ole
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical analysis
Mathematics - Classical Analysis and ODEs
Mathematics - Combinatorics
Polynomials
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Beschreibung
Zusammenfassung:We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case.
ISSN:2331-8422
DOI:10.48550/arxiv.0905.4033