Fourier Series and Orthogonal Polynomials

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Courier Corporation, 2004 - Mathematics - 234 pages
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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
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