Periodic Differential Equations

Periodic Differential Equations

An Introduction to Mathieu, Lamé, and Allied Functions

1st Edition - January 1, 1964

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  • Author: F. M. Arscott
  • eBook ISBN: 9781483164885

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Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation. This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and the principles of asymptotic expansions. These topics are followed by discussions of the stable and unstable solutions of Mathieu's general equation; general properties and characteristic exponent of Hill's equation; and the general nature and solutions of the spheroidal wave equation. The concluding chapters explore the polynomials, orthogonality properties, and integral relations of Lamé's equation. These chapters also describe the wave functions and solutions of the ellipsoidal wave equation. This book will prove useful to pure and applied mathematicians and functional analysis.

Table of Contents

  • Preface

    I Formation of the Equations: The Main Problems

    II Mathieu's Equation — General Theory

    III Mathieu Functions of Integral Order

    IV Mathieu Functions of Integral Order — Further Properties

    V Asymptotic Expansions

    VI Mathieu's General Equation

    VII Hill's Equation

    VIII The Spheroidal Wave Equation

    IX Lamé's Equation

    X The Ellipsoidal Wave Equation

    Appendix A — Bessel Functions

    Appendix B — Legendre, Gegenbauer and Tchebycheff Functions

    Appendix C — Elliptic Functions


    Additional Notes


    Other Volumes in the Series in Pure and Applied Mathematics

Product details

  • No. of pages: 294
  • Language: English
  • Copyright: © Pergamon 1964
  • Published: January 1, 1964
  • Imprint: Pergamon
  • eBook ISBN: 9781483164885

About the Author

F. M. Arscott

About the Editors

I. N. Sneddon

M. Stark

S. Ulam

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