Periodic Differential Equations

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.

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

References

Additional Notes

Index

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