Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 General Overview of Multivariable Special Functions
- 2 Orthogonal Polynomials of Several Variables
- 3 Appell and Lauricella Hypergeometric Functions
- 4 A-Hypergeometric Functions
- 5 Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
- 6 Elliptic Hypergeometric Functions Associated with Root Systems
- 7 Dunkl Operators and Related Special Functions
- 8 Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
- 9 Macdonald–Koornwinder Polynomials
- 10 Combinatorial Aspects of Macdonald and Related Polynomials
- 11 Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
- 12 9 j-Coefficients and Higher
- Index
6 - Elliptic Hypergeometric Functions Associated with Root Systems
Published online by Cambridge University Press: 30 September 2020
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 General Overview of Multivariable Special Functions
- 2 Orthogonal Polynomials of Several Variables
- 3 Appell and Lauricella Hypergeometric Functions
- 4 A-Hypergeometric Functions
- 5 Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
- 6 Elliptic Hypergeometric Functions Associated with Root Systems
- 7 Dunkl Operators and Related Special Functions
- 8 Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
- 9 Macdonald–Koornwinder Polynomials
- 10 Combinatorial Aspects of Macdonald and Related Polynomials
- 11 Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
- 12 9 j-Coefficients and Higher
- Index
Summary
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.
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- Encyclopedia of Special Functions: The Askey-Bateman Project , pp. 159 - 186Publisher: Cambridge University PressPrint publication year: 2020
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