Chapter 10 - Mathematical Series

Abstract

A mathematical series is a sum of terms, either with a finite number of terms or an infinite number of terms. There is generally a rule for generating the terms. A constant series has terms that are constants, and a functional series has terms that are constants times members of a set of basis functions. An infinite series converges if the sum approaches a finite limit ever more closely as ever more terms are summed. A Maclaurin series is a functional series with basis functions that are power of x, where x is the independent variable. A Taylor series is a functional series with basis functions that are powers of x−h, where h is a constant. An infinite power series can represent a function within a region inside which it converges. Under certain conditions mathematical operations on a series are equivalent to mathematical operations on the terms of the series. Power series in several independent variables can exist.