Well we need the Taylor series about 0.

So lets look at the sequence of derivatives and find the first three which are non-zero.

First the zero-th drrivative is non-zeros at and equal to

The first derivative:

which is zero at

Second derivative:

which is equal to at

Third derivative:

which is zero at

Fourth derivative:

which is when .

So the series expansion of to the first three non zero terms is:

so (if I have done this right):

RonL