Elliptic hypergeometric series on root systems

2002/07/04 by Hjalmar Rosengren
Mathematics · #math.CA #math.QA #msc:33D67 #msc:11F50

paper · pdf

published as Adv. Math. 181 (2004), 417-447 · 27 pages

arxiv created 2002/07/04 · arxiv updated 2009/11/30

Abstract

We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems A_n, C_n and D_n. In the special cases of classical and q-series, our approach leads to new elementary proofs of the corresponding identities.

Related

• Hypergeometric and basic hypergeometric series and integrals associated with root systems
• Expansion formulas for multiple basic hypergeometric series over root systems
• Karlsson-Minton type hypergeometric functions on the root system C_n
• Expansion formulas for elliptic hypergeometric series
• Duality transformation formulas for multiple elliptic hypergeometric series of type BC