Encyclopedia of Special Functions: The Askey-Bateman Project

doi:10.1017/9780511777165

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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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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List of Contributors
pp ix-x
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Preface
pp xi-xii
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1 - General Overview of Multivariable Special Functions
pp 1-18
- By T. H. Koornwinder, J. V. Stokman
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2 - Orthogonal Polynomials of Several Variables
pp 19-78
- By Yuan Xu
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3 - Appell and Lauricella Hypergeometric Functions
pp 79-100
- By K. Matsumoto
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4 - A-Hypergeometric Functions
pp 101-121
- By N. Takayama
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5 - Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
pp 122-158
- By M. J. Schlosser
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6 - Elliptic Hypergeometric Functions Associated with Root Systems
pp 159-186
- By H. Rosengren, S. O. Warnaar
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7 - Dunkl Operators and Related Special Functions
pp 187-216
- By C. F. Dunkl
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8 - Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
pp 217-257
- By G. J. Heckman, E. M. Opdam
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9 - Macdonald–Koornwinder Polynomials
pp 258-313
- By J. V. Stokman
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10 - Combinatorial Aspects of Macdonald and Related Polynomials
pp 314-367
- By J. Haglund
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11 - Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
pp 368-401
- By V. Tarasov, A. Varchenko
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12 - 9 j-Coefficients and Higher
pp 402-419
- By J. Van der Jeugt
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Index
pp 420-428
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Encyclopedia of Special Functions: The Askey-Bateman Project

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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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