Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 1, Univariate Orthogonal Polynomials

Mourad E. H. Ismail, Walter Van Assche

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN:
  9780521197427
• eBook ISBN:
  9781108764339
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title page
• Title page
• Copyright page
• Contents
• List of Contributors
• Preface
• 1 Preliminaries
• 2 General Orthogonal Polynomials
• 3 Jacobi and Related Polynomials
• 4 Recursively Defined Polynomials
• 5 Wilson and Related Polynomials
• 6 Discrete Orthogonal Polynomials
• 7 Some q-Orthogonal Polynomials
• 8 The Askey–Wilson Family of Polynomials
• 9 Orthogonal Polynomials on the Unit Circle
• 10 Zeros of Orthogonal Polynomials
• 11 The Moment Problem
• 12 Matrix-Valued Orthogonal Polynomials and Differential Equations
• 13 Some Families of Matrix-Valued Jacobi Orthogonal Polynomials
• References
• Index