Encyclopedia of Special Functions: The Askey-Bateman Project

Walter Van Assche

doi:10.1017/9780511979156

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Mañas, Manuel Fernández‐Irisarri, Itsaso and González‐Hernández, Omar F. 2022. Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations. Studies in Applied Mathematics, Vol. 148, Issue. 3, p. 1141.

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Loginov, Kirill 2022. Numerical Solution of the Problem of Filtering Estimates Information Impact on the Electorate. Informatics and Automation, Vol. 21, Issue. 3, p. 624.

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Mañas, Manuel 2022. Pearson equations for discrete orthogonal polynomials: III—Christoffel and Geronimus transformations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Vol. 116, Issue. 4,

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Luo, Min-Jie Krishna Raina, Ravinder and Zhao, Shu-Han 2022. Certain results on generating functions related to the associated Meixner-Pollaczek polynomials. Integral Transforms and Special Functions, Vol. 33, Issue. 6, p. 496.

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Fernández‐Irisarri, Itsaso and Mañas, Manuel 2023. Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials. Studies in Applied Mathematics, Vol. 151, Issue. 2, p. 509.

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Polansky, Ivan and Loginov, Kirill 2023. Optimal Nonlinear Filtering of Information Impact Estimates in a Stochastic Model of Information Warfare. Informatics and Automation, Vol. 22, Issue. 4, p. 745.

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Volume 1: Univariate Orthogonal Polynomials
Edited by Mourad E. H. Ismail, University of Central Florida
Assisted by Walter Van Assche, Katholieke Universiteit Leuven, Belgium

Publisher:: Cambridge University Press
Online publication date:: September 2020
Print publication year:: 2020
Online ISBN:: 9780511979156
DOI:: https://doi.org/10.1017/9780511979156

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

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This is the first of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 1 contains most of the material on orthogonal polynomials, from the classical orthogonal polynomials of Hermite, Laguerre and Jacobi to the Askey–Wilson polynomials, which are the most general basic hypergeometric orthogonal polynomials. Separate chapters cover orthogonal polynomials on the unit circle, zeros of orthogonal polynomials and matrix orthogonal polynomials, with detailed results about matrix-valued Jacobi polynomials. A chapter on moment problems provides many examples of indeterminate moment problems. A thorough bibliography rounds off what will be an essential reference.

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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

Contributors
pp ix-x

Preface
pp xi-xiv

1 - Preliminaries
pp 1-15

2 - General Orthogonal Polynomials
pp 16-50

3 - Jacobi and Related Polynomials
pp 51-99

4 - Recursively Defined Polynomials
pp 100-118

5 - Wilson and Related Polynomials
pp 119-128

6 - Discrete Orthogonal Polynomials
pp 129-156

7 - Some q-Orthogonal Polynomials
pp 157-177

8 - The Askey–Wilson Family of Polynomials
pp 178-198

9 - Orthogonal Polynomials on the Unit Circle
pp 199-241

10 - Zeros of Orthogonal Polynomials
pp 242-268

11 - The Moment Problem
pp 269-306

12 - Matrix-Valued Orthogonal Polynomials and Differential Equations
pp 307-333

13 - Some Families of Matrix-Valued Jacobi Orthogonal Polynomials
pp 334-356

References
pp 357-384

Index
pp 385-388

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