It is well known th a t an infinitely differentiable function f ( x ) can be ex panded in a Taylor series around a point Xq in the interval where it is defined. This series has the form
OO f ( x ) ~ ^ 2 c n (x - x 0)n, (2.1)
where the coefficients cn are given by
n — 1,2.......Cn, — n! J dx
If certain conditions are satisfied, then the above series converges to / pointwise (that is, a t every point x) in an open interval centered at xq, and we can use the equality sign between the two sides in (2.1).