A Treatise on

Bessel FunctionsAnd Their Applications to Physics

Bessel FunctionsAnd Their Applications to Physics

This book has been written in view of the great and growing importance of the Bessel functions in almost every branch of mathematical physics; and its principal object is to supply in a convenient form so much of the theory of the functions as is necessary for their practical application, and to illustrate their use by a selection of physical problems, worked out in some detail.

Some readers may be inclined to think that the earlier chapters contain a needless amount of tedious analysis; but it must be remembered that the properties of the Bessel functions are not without an interest of their own on purely mathematical grounds, and that they afi'ord excellent illustrations of the more recent theory of differential equations, and of the theory of a complex variable. And even from the purely physical point of View it is impossible to say that an analytical formula is useless for practical purposes; it may be so now, but experience has repeatedly shown that the most abstract analysis may unexpectedly prove to be of the highest importance in mathematical physics. As a matter of fact it will be found that little, if any, of the analytical theory included in the present work has failed to be of some use or other in the later chapters; and we are so far from thinking that anything superﬂuous has been inserted, that we could almost wish that space would have allowed of a more extended treatment, especially in the chapters on the complex theory and on definite integrals.

PIBN | 10033108 |

ISBN | 978-1-330-12995-1 |

ISBN (Hardcover) | 978-1-5281-6039-1 |

Language | English |

Category | Calculus |

Pages | 305 |

Words | 43687 |

Vocabulary | 1475 |

Elements of the

Infinitesimal

CalculusWith Numerous Examples

and Applications to Analysis

Infinitesimal

CalculusWith Numerous Examples

and Applications to Analysis

Graphical

Calculus

Calculus

Hyperbolic

Functions

Functions

Theory of

Electricity

and Magnetism

Electricity

and Magnetism

A Manual of

Quaternions

Quaternions

Vector

AnalysisAn Introduction to Vector-Methods and Their

Various Applications to Physics and Mathematics

AnalysisAn Introduction to Vector-Methods and Their

Various Applications to Physics and Mathematics

Solutions of

the Examples

in a Treatise on

Differential

Equations

the Examples

in a Treatise on

Differential

Equations

Developments

Obtained by

Cauchy's TheoremWith Applications to

the Elliptic Functions

Obtained by

Cauchy's TheoremWith Applications to

the Elliptic Functions

A Brief History

of MathematicsAn Authorized Translation of Dr. Karl Fink's

Geschichte Der Elementar-Mathematik

of MathematicsAn Authorized Translation of Dr. Karl Fink's

Geschichte Der Elementar-Mathematik

Lectures on

MathematicsDelivered From Aug. 28 to Sept. 9, 1893 Before Members of the

Congress of Mathematics Held in Connection With the World's

Fair in Chicago at Northwestern University, Evanston, Ill

MathematicsDelivered From Aug. 28 to Sept. 9, 1893 Before Members of the

Congress of Mathematics Held in Connection With the World's

Fair in Chicago at Northwestern University, Evanston, Ill

Introduction

to QuaternionsWith Numerous Examples

to QuaternionsWith Numerous Examples

Manual of

Geometrical and

Infinitesimal

Analysis

Geometrical and

Infinitesimal

Analysis

An Elementary

Course in

Differential

Equations

Course in

Differential

Equations

Complex Roots

of Polynomial

Equations

of Polynomial

Equations

Harmonic

Functions

Functions

A Treatise on the

Integral CalculusWith Applications,

Examples, and Problems

Vol. 2

Integral CalculusWith Applications,

Examples, and Problems

Vol. 2

Differential

and Integral

Calculus

and Integral

Calculus

A Treatise on

Bessel FunctionsAnd Their Applications to Physics

Bessel FunctionsAnd Their Applications to Physics

A Treatise on

the Calculus

of Finite

Differences

the Calculus

of Finite

Differences

An Elementary

Treatise on the

Differential CalculusFounded on the Method

of Rates or Fluxions

Treatise on the

Differential CalculusFounded on the Method

of Rates or Fluxions

A Treatise on

the Circle and

the Sphere

the Circle and

the Sphere

An

Introduction

to Mathematics

Introduction

to Mathematics

The

Calculus for

Engineers

Calculus for

Engineers

A Treatise

on Plane

Trigonometry

on Plane

Trigonometry

Plane

Trigonometry

Trigonometry

Eight Lectures on

Theoretical PhysicsDelivered at Columbia

University in 1909

Theoretical PhysicsDelivered at Columbia

University in 1909

A New Treatise on

the Elements of the

Differential and

Integral Calculus

the Elements of the

Differential and

Integral Calculus

Elements of

Vector AnalysisArranged for the Use

of Students in Physics

Vector AnalysisArranged for the Use

of Students in Physics

The

Nature of

Mathematics

Nature of

Mathematics

Archimedes

A History of

Mathematics

Mathematics

Elements of the

Integral CalculusWith a Key to the Solution of Differential

Equations, and a Short Table of Integrals

Integral CalculusWith a Key to the Solution of Differential

Equations, and a Short Table of Integrals

A Treatise on

Electricity

and Magnetism

Vol. 1

Electricity

and Magnetism

Vol. 1

AlgebraAn Elementary Text-Book for the Higher

Classes of Secondary Schools and for Colleges

Vol. 2

Classes of Secondary Schools and for Colleges

Vol. 2

The Philosophy

of MathematicsTranslated From the Cours De

Philosophie Positive of Auguste Comte

of MathematicsTranslated From the Cours De

Philosophie Positive of Auguste Comte

A Treatise on

Differential

EquationsSupplementary Volume

Differential

EquationsSupplementary Volume

Spherical

TrigonometryFor Colleges and Secondary Schools

TrigonometryFor Colleges and Secondary Schools

Calculus

Elements of the

Differential and

Integral CalculusMethod of Rates

Differential and

Integral CalculusMethod of Rates

Rapid

ArithmeticQuick and Special Methods in Arithmetical

Calculation, Together With a Collections

of Puzzles and Curiosities of Numbers

ArithmeticQuick and Special Methods in Arithmetical

Calculation, Together With a Collections

of Puzzles and Curiosities of Numbers

A Treatise on the

Integral Calculus

and Its ApplicationsWith Numerous Examples

Integral Calculus

and Its ApplicationsWith Numerous Examples

General Investigations

of Curved Surfaces

of 1827 and 1825Translated With Notes

and a Bibliography

of Curved Surfaces

of 1827 and 1825Translated With Notes

and a Bibliography

Elements of

Quaternions

Vol. 1

Quaternions

Vol. 1

Theory of

Functions of a

Complex Variable

Functions of a

Complex Variable

On the Representation

of a Function by a

Trigonometric SeriesDissertation Presented to the Board of University

Studies of the Johns Hopkins University

for the Degree of Doctor of Philosophy

of a Function by a

Trigonometric SeriesDissertation Presented to the Board of University

Studies of the Johns Hopkins University

for the Degree of Doctor of Philosophy

A Potential Problem

Connected With

an Infinite Dock in

a Running Stream

Connected With

an Infinite Dock in

a Running Stream

An Elementary

Treatise on the

Differential and

Integral Calculus

Treatise on the

Differential and

Integral Calculus

AlgebraAn Elementary Text-Book for the Higher

Classes of Secondary Schools and for Colleges

Vol. 2

Classes of Secondary Schools and for Colleges

Vol. 2

Treatise on

Trigonometry

Trigonometry

The Method of

Fluxions and

Infinite SeriesWith Its Application to the

Geometry of Curve-Lines

Fluxions and

Infinite SeriesWith Its Application to the

Geometry of Curve-Lines

History of

Modern

Mathematics

Modern

Mathematics

Vector

Analysis and

Quaternions

Analysis and

Quaternions

Forward Scattering

of High-Frequency

Plane Waves

by a Sphere

of High-Frequency

Plane Waves

by a Sphere