Encyclopedia of Special Functions: The Askey-Bateman Project

doi:10.1017/9780511777165

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Chestnov, Vsevolod Matsubara-Heo, Saiei J. Munch, Henrik J. and Takayama, Nobuki 2023. Restrictions of Pfaffian systems for Feynman integrals. Journal of High Energy Physics, Vol. 2023, Issue. 11,

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Yamaguchi, Kohei and Yanagida, Shintarou 2023. Specializing Koornwinder polynomials to Macdonald polynomials of type B, C, D and BC. Journal of Algebraic Combinatorics, Vol. 57, Issue. 1, p. 171.

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Ball, Adam De, Shounak Srikant, Akshay Yelleshpur and Volovich, Anastasia 2024. Scalar-graviton amplitudes and celestial holography. Journal of High Energy Physics, Vol. 2024, Issue. 2,

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Volume 2: Multivariable Special Functions
Edited by Tom H. Koornwinder, Universiteit van Amsterdam, Jasper V. Stokman, Universiteit van Amsterdam

Publisher:: Cambridge University Press
Online publication date:: September 2020
Print publication year:: 2020
Online ISBN:: 9780511777165
DOI:: https://doi.org/10.1017/9780511777165

Subjects:: Mathematics, Abstract Analysis, Numerical Analysis and Computational Science

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This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

‘Overall the volume is a very useful addition to any research mathematician’s library who works on these topics.’

Manjil Pratim Saikia Source: zbMATH

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Encyclopedia of Special Functions: The Askey-Bateman Project

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

List of Contributors
pp ix-x

Preface
pp xi-xii

1 - General Overview of Multivariable Special Functions
pp 1-18

2 - Orthogonal Polynomials of Several Variables
pp 19-78

3 - Appell and Lauricella Hypergeometric Functions
pp 79-100

4 - A-Hypergeometric Functions
pp 101-121

5 - Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
pp 122-158

6 - Elliptic Hypergeometric Functions Associated with Root Systems
pp 159-186

7 - Dunkl Operators and Related Special Functions
pp 187-216

8 - Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
pp 217-257

9 - Macdonald–Koornwinder Polynomials
pp 258-313

10 - Combinatorial Aspects of Macdonald and Related Polynomials
pp 314-367

11 - Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
pp 368-401

12 - 9 j-Coefficients and Higher
pp 402-419

Index
pp 420-428

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Encyclopedia of Special Functions: The Askey-Bateman Project

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