Series, Taylor — Maclaurin Series

Abstract

By a series we mean a set of numbers a₁, a₂, a₃… such that we have a rule for calculating a₂, a₃ etc. from the first number a₁.Series occur in many problems in chemistry such as specific heats of solids, the theory of black-body radiation, solution of the Schrödinger equation, statistical thermodynamics and Fourier series in X-ray crystallography. In this chapter we consider the summation of series and the convergence of infinite series. We shall develop methods for the expansion of functions such as transcendental functions in terms of infinite series.