Handbook of Series for Scientists and Engineers e-bog

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.