Expressing functions as infinite series Power Series Expressing functions as infinite series

Basic Ideas… Assume that a function f(x) can be expanded as a power series and that you know the value of f(x) and its derivatives at x = a The coefficients will depend on the nature of the function

You can determine the coefficients by differentiating and letting x = a:

A fundamental result… Any continuous, differentiable function can be “re-cast” as: This is also known as the Taylor Series or Taylor Expansion

The Maclaurin Series (a = 0) Examples: sin(x) ex