Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 037, 11 pages      arXiv:1701.08960
Contribution to the Special Issue on Elliptic Hypergeometric Functions and Their Applications

Gustafson-Rakha-Type Elliptic Hypergeometric Series

Hjalmar Rosengren
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden

Received February 02, 2017, in final form May 29, 2017; Published online June 01, 2017

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.

Key words: elliptic hypergeometric series; multivariable hypergeometric series; Jackson summation; Bailey transformation.

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