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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Authors: Langer, R., Schlosser, M.J., Warnaar, S.O.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149148
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture / R. Langer, M.J. Schlosser, S.O. Warnaar // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ.

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,...