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[Wiley Series in Probability and Statistics] Advanced Calculus with Applications in Statistics || Orthogonal Polynomials

✍ Scribed by Khuri, André I.

Publisher
John Wiley & Sons, Inc.
Year
2002
Tongue
English
Weight
248 KB
Category
Article
ISBN-13
9780471394884

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✦ Synopsis

Polynomials

The subject of orthogonal polynomials can be traced back to the work of the Ž . French mathematician Adrien-Marie Legendre 1752᎐1833 on planetary motion. These polynomials have important applications in physics, quantum mechanics, mathematical statistics, and other areas in mathematics.

This chapter provides an exposition of the properties of orthogonal polynomials. Emphasis will be placed on Legendre, Chebyshev, Jacobi, Laguerre, and Hermite polynomials. In addition, applications of these polynomials in statistics will be discussed in Section 10.9.

s 0 for all m / n, then S forms a sequence of polynomials orthogonal with Ž . respect to w x .

A sequence of orthogonal polynomials can be constructed on the basis of the following theorem

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[Wiley Series in Probability and Statist
[Wiley Series in Probability and Statistics] Advanced Calculus with Applications in Statistics || Wiley Series in Probability and Statistics
✍ Khuri, André I. 📂 Article 📅 2002 🏛 John Wiley & Sons, Inc. 🌐 English ⚖ 359 KB 👁 2 views

The Wiley Series in Probability and Statistics is well established and authoritative. It covers many topics of current research interest in both pure and applied statistics and probability theory. Written by leading statisticians and institutions, the titles span both state-of-the-art developments i