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Zbl 1066.33017
Rosengren, Hjalmar
Elliptic hypergeometric series on root systems. (English)
[J] Adv. Math. 181, No. 2, 417-447 (2004). ISSN 0001-8708

The author studies elliptic hypergeometric series on root systems. He obtains elliptic analogues for the Gustafson--Milne type series on the root systems $A_n$, $C_n$ and $D_n$. In the case of root systems $A_n$ and $D_n$ the proof is based on an elliptic partial fraction expansion and an induction. For this root system $C_n$ the multivariable hypergeometric summations are obtained through convenient determinant evaluations. The main formula is deduced as a special case of a multivariable Jackson sum of {\it S. O. Warnaar} [Constructive Approximation, 18, 479-502 (2002; Zbl 1040.33013)]. From these summation and transformation formulas there are deduced corresponding elliptic Bailey transformations.
[Doru Ştefănescu (Bucureşti)]

MSC 2000:: *33D67 Basic hypergeometric functions associated with root systems
11F50 Jacobi forms

Keywords: elliptic hypergeometric series; hypergeometric series on root systems; Jackson summation; Bailey transforms

Citations: Zbl 1040.33013

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Zentralblatt MATH Berlin [Germany]