Infinitely Differentiable But Not Analytic Function At A Point

We give an example of a function which is infinitely differentiable, but not analytic at the point x = 0. This means that we can calculate the n^th derivative at x = 0 for n = 1, 2, 3,... but the Taylor series about the point x = 0 doesn`t converge to the function value, for x in a small neighbourhood of 0. This example is taken from my Master`s dissertation.