What is the power series for cos(u^2) up to the u^24 term?

[iceman]

Hello, can anyone help me on this one? I am finding problem pretty tricky indeed.

I know the power series (or Taylor series) for cosx is

1-x^2/2!+x^4/4!-x^6/6!+... (It is convergent for all element x is a member of set R)

Q) Write down the power series for cos(u^2) up to the u^24 term.

Your help is kindly appreciated.

 

[selfAdjoint]

First write the cos(x) series you know. Then plug in u^2 for each x in the series. What will that do to the powers of u? What will it do to the coefficients? After you answer those questions try this. What will be the factorial in the denominator when the power of u is 24?