Gustafson-Rakha-Type Elliptic Hypergeometric Series

[摘要] We prove a multivariable elliptic extension of Jackson's summation formula conjectured by Spiridonov. The trigonometric limit case of this result is due to Gustafson and Rakha. As applications, we obtain two further multivariable elliptic Jackson summations and two multivariable elliptic Bailey transformations. The latter four results are all new even in the trigonometric case.

[关键词] elliptic hypergeometric series;multivariable hypergeometric series;Jackson summation;Bailey transformation