Question

How do you find the Maclaurin series of `f(x)=cos(x^2)` ?

Answer 1

We have the Maclaurin series
`cosx=sum_{n=0}^infty(-1)^n{x^{2n}}/{(2n)!}`

by replacing `x` by `x^2`,
`cos(x^2)=sum_{n=0}^infty(-1)^n{x^{4n}}/{(2n)!}`