Elliptic hypergeometric functions associated with root systems
Book chapter, 2020

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two in essence form an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integrals and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson). We survey the main properties of elliptic BC_n interpolation functions and BC_n-symmetric biorthogonal functions, which generalize Okounkov's BC_n interpolation Macdonald polynomials and the Koornwinder polynomials, respectively.

elliptic hypergeometric functions

hypergeometric functions associated with root systems

elliptic Selberg integrals

elliptic BC_n-symmetric biorthogonal functions

elliptic interpolation functions

affine root systems


Hjalmar Rosengren

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Ole Warnaar

University of Queensland

Multivariable Special Functions

9780511777165 (ISBN)

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