# Fourier Series and Orthogonal Polynomials

Courier Corporation, 2004 - Mathematics - 234 pages
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followed by chapters on orthogonal, Jacobi, Hermite, and Laguerre polynomials, and the text concludes with a chapter on convergence. 1941 edition.

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### Contents

 FOURIER SERIES 1 LEGENDRE POLYNOMIALS 45 BESSEL FUNCTIONS 69 BOUNDARY VALUE PROBLEMS 91 DOUBLE SERIES LAPLACE SERIES 115 THE PEARSON FREQUENCY FUNCTIONS 142
 ORTHOGONAL POLYNOMIALS 149 JACOBI POLYNOMIALS 166 HERMITE POLYNOMIALS 176 LAGUERRE POLYNOMIALS 184 CONVERGENCE 191 Copyright