For unlimited access to Class Notes, a Class+ subscription is required.

Section Taylor and McLaren series

Two big question:

What functions have power series representations and how can we find them?

Suppose has a power series of a with radius ; that is,

If

Differentiating, we get:

If

Repeating:

If .

Derivative

If

If

In general, it seems that

Theorem:

If has a power series expansion (or representation at that is, if

then the coefficients are given by,

Replacing in the formula, we have