Book contents
- Frontmatter
- Contents
- 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
10 - Zeros of Orthogonal Polynomials
Published online by Cambridge University Press: 14 September 2020
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Book contents
- Frontmatter
- Contents
- 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
Summary
We begin by outlining some methods for getting information on zeros of orthogonal polynomials. Some of the main ones depend on the orthogonality measure, the recurrence relation and, if available, the differential equation for the polynomials.
In Section 10.2 we give results obtained by these methods for general classes of orthogonal polynomials. Sections 10.3 to 10.8 give specific applications to, and special results for, Jacobi, ultraspherical, Legendre, Laguerre, Hermite, and other polynomials.
Other chapters contain material on zeros. Zeros of Bessel polynomials are discussed in Section 3.13.
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- Encyclopedia of Special Functions: The Askey-Bateman Project , pp. 242 - 268Publisher: Cambridge University PressPrint publication year: 2020