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
8 - Jacobi Polynomials and 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
In this chapter the basic theory of hypergeometric functions for root systems is discussed, together with some of its applications. These functions arise in various contexts such as the representation theory of reductive groups, multivariate orthogonal polynomials, harmonic analysis on symmetric spaces, integrable models in mathematical physics, Dunkl operators, Knizhnik-Zamolodchikov connections, affine Hecke algebras, algebraic combinatorics (e.g. the Macdonald conjectures), the determination of certain Bernstein-Sato polynomials and period integrals for moduli of Del Pezzo surfaces.
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- Information
- Encyclopedia of Special Functions: The Askey-Bateman Project , pp. 217 - 257Publisher: Cambridge University PressPrint publication year: 2020
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