Handbook of Series for Scientists and Engineers

Handbook of Series for Scientists and Engineers is a handbook of mathematical series for scientists and engineers and includes tables analogous to tables of integrals. The method of expanding a function in a series is described, and the most common expansions and sums are given. Most of the series are valid for complex values of the variable, and the symbols z, ?, ? always denote a complex variable. A glossary of symbols is included.

Comprised of three parts, this book begins with an introduction to some basic rules for operations with series, focusing on convergence tests and operations with convergent series. Expansion methods and some summation methods are also considered. The second part focuses on the expansions of frequently used functions in various series, and includes chapters that discuss rational and irrational algebraic expressions; trigonometric functions and logarithmic functions; exponential functions and hyperbolic functions; and Legendre polynomials and functions. The third part lists sums of series, arranged according to the features of the general term in the series, such as series involving only natural numbers; series of algebraic functions; series of Bessel functions and related functions; and series of Legendre functions.

This monograph is intended for scientists and engineers as well as mathematicians.

Preface

Part I. Introduction

1. Properties of Series

A. Convergence Tests

B. Operations with Convergent Series

2. Expansion Methods

3. Some Summation Methods

Part II. Functions Expanded in Series

1. Rational Algebraic Expressions

2. Irrational Algebraic Expressions

3. Trigonometric Functions

A. Sine Functions

B. Cosine Functions

C. Other Trigonometric Functions

4. Inverse Trigonometric Functions

5. Logarithmic Functions

6. Exponential Functions

7. Hyperbolic Functions

8. Inverse Hyperbolic Functions

9. Bessel Functions of the First Kind

10. Other Bessel Functions and Related Functions

11. Legendre Polynomials and Functions

12. Other Functions

Part III. Sums of Series

1. Series Involving Only Natural Numbers

A. Inverse and Other Products of Natural Numbers

B. Factorials and Gamma Functions

C. Other Infinite Series

D. Finite Series

2. Series of Algebraic Functions

A. Power Series

B. Series Involving Other Rational Functions

C. Other Series

D. Finite Series Involving Rational Functions

3. Trigonometric Series

A. Terms Containing Only Products of Natural Numbers

B. Terms Also Containing Powers of Other Variables

C. Terms Containing Rational Functions other than Powers

D. Series Containing Two or More Trigonometric Functions

E. Other Infinite Series

F. Finite Series

4. Series of Bessel Functions and Related Functions

A. Neumann Series

B. Kapteyn Series

C. Fourier-Bessel and Dini Series

D. Schlömilch Series

E. Other Series

5. Series of Legendre Functions

A. Terms Containing Only One Legendre Polynomial

B. Terms Containing Two Legendre Functions

C. Terms Also Containing Powers of Other Variables

D. Terms Also Containing Other Functions

6. Miscellaneous Series

List of Symbols

References