Lets suppose that the McLaurin expansion of exists and write...

(1)

In this case we can derive the from the McLaurin expansion of ...

(2)

... where for even and for odd. If we write the product of the series (1) and (2) we obtain...

(3)

... and from (3) we obtain...

The McLaurin expansion of with maximum exponent 4 is then...

(4)

Kind regards