Provided certain conditions are met, we can expand the function f(x) in an infinite power series about the point x = a:

Differentiate (4.84) m times, and then set x = a to show that cn = f(n)(a)/n!, thus giving the familiar Taylor series:

f(x) = (x-a)" (4.84) n=0 f(x)-y(n)(a) n=0 n! (4.85)