Basic Equations And Special Functions Of Mathematical Physics

381 Pages·1968·7.113 MB·English

by  V. Ya. Arsenin

V. Ya. Arsenin
Basic Equations
and
Special Functions
of
Mathematical Physics

Jl

Basic Equations and Special
Functions of Mathematical Physics
T
BASIC EQUATIONS AND SPECIAL
FUNCTIONS OF MATHEMATICAL PHYSICS
V. Ya. Arsenin
Translated by
S. Chomet, King’s College, London
English translation edited by
S. Doniach, Imperial College of
Science and Technology, London
LONDON ILIFFE BOOKS LTD
NEW YORK AMERICAN ELSEVIER PUBLISHING
COMPANY INC.
First published by Nauka, Moscow, under the title Matematicheskaya
Fizika — Osnovnye Uravneniya i Spctsial’nye Funktsii
English Edition first published in 1968 by Jliffc Books Ltd,
42 Russel] Square, London, W.C.I.
American edition published by American Elsevier Publishing Company Inc.
52 Vanderbilt Avenue, New York, New York 10017
Library of Congress Catalog Card Number 68-57390
Translated and prepared for press by Scripta Technica Ltd,
139a New Bond Street, London, W.l.
(C) Iliffe Books Ltd 1968
Printed in Poland
Contents
Preface 7
PART 1
Chapter 1 Linear Equations with Two Independent Variables 3
Chapter 2 Partial Differential Equations in Physics.
Boundary-value Problems 13
Chapter 3 The Method of Characteristics 32
Chapter 4 Separation of Variables (Fourier Method) 59
Chapter 5 The Method of Green’s Functions for Parabolic
Equations 107
Chapter 6 The Method of Green’s Functions for Elliptical
Equations 124
Chapter 7 Potentials 146
Chapter 8 Integral Equations 168
Chapter 9 Integral Equations with Symmetric Kernels 188
PART 2
Chapter 10 Gamma Function 215
Chapter 11 Cylindrical Functions 223
Chapter 12 Spherical Harmonics 268
Chapter 13 Chebyshev-Hermite and Chebyshev-Laguerre
Polynomials 291
Appendix Definition of Generalised Functions. The S
Function 303
Answers and Solutions 321
Bibliography 355
Index 357
5 A