eBook ISBN:  9781614440062 
Product Code:  CAR/6.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
eBook ISBN:  9781614440062 
Product Code:  CAR/6.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 

Book DetailsThe Carus Mathematical MonographsVolume: 6; 1941; 234 pp
The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics.
The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence.
There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.

Table of Contents

Chapters

Chapter I. Fourier series

Chapter II. Legendre polynomials

Chapter III. Bessel functions

Chapter IV. Boundary value problems

Chapter V. Double series; Laplace series

Chapter VI. The Pearson frequency functions

Chapter VII. Orthogonal polynomials

Chapter VIII. Jacobi polynomials

Chapter IX. Hermite polynomials

Chapter X. Laguerre polynomials

Chapter XI. Convergence


Additional Material

Reviews

The author has been able, by not proving everything, to include a great deal of interesting material; by proving typical results in detail, he has shown how the formal results may be justified and safely used. Considerable attention is paid to physical applications of orthogonal functions. This rather unusual synthesis of two different attitudes should be good for students beginning advanced work in either pure or applied analysis.
R. P. Boas, Jr., Mathematical Reviews


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The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics.
The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence.
There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.

Chapters

Chapter I. Fourier series

Chapter II. Legendre polynomials

Chapter III. Bessel functions

Chapter IV. Boundary value problems

Chapter V. Double series; Laplace series

Chapter VI. The Pearson frequency functions

Chapter VII. Orthogonal polynomials

Chapter VIII. Jacobi polynomials

Chapter IX. Hermite polynomials

Chapter X. Laguerre polynomials

Chapter XI. Convergence

The author has been able, by not proving everything, to include a great deal of interesting material; by proving typical results in detail, he has shown how the formal results may be justified and safely used. Considerable attention is paid to physical applications of orthogonal functions. This rather unusual synthesis of two different attitudes should be good for students beginning advanced work in either pure or applied analysis.
R. P. Boas, Jr., Mathematical Reviews