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
1 - General Overview of Multivariable Special Functions
Published online by Cambridge University Press: 30 September 2020
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
Summary
This chapter gives an introduction to the book. It surveys multivariable hypergeometric series and integrals, with comparison of the classical, basic and elliptic case, and multivariable (bi)orthogonal polynomials and functions, where root system generalizations of classical orthogonal polynomials get special emphasis. The chapter also provides a global description of the other chapters.
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- Publisher: Cambridge University PressPrint publication year: 2020