- #1

ptolema

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## Homework Statement

Let A(x) = a

_{0}+ a

_{1}x + a

_{2}x

^{2}+ a

_{3}x

^{3}+ ... = Ʃa

_{n}x

^{n}.

Express E(x) = a

_{0}+ a

_{2}x

^{2}+ a

_{4}x

^{4}+ ... = Ʃa

_{2n}x

^{2n}.

Do the same for O(x) = a

_{1}x + a

_{3}x

^{3}+ a

_{5}x

^{5}+ ...

## Homework Equations

A(x) = a

_{0}+ a

_{1}x + a

_{2}x

^{2}+ a

_{3}x

^{3}+ ... = Ʃa

_{n}x

^{n}

## The Attempt at a Solution

So I tried using A(x

^{2}) as a starting point, but got stuck on how to get the coefficients of A(x

^{2}) = a

_{0}+ a

_{1}x

^{2}+ a

_{2}x

^{4}+ a

_{3}x

^{6}+ ... to match those of E(x).

How would I begin expressing E(x) and O(x) in terms of A(x)? Could there be something I could do with sin or cos?