- #1

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## Homework Statement

(f*g)(x) = integral from -pi to pi of (f(y)g(x-y))dy

f(x) = ∑c

_{n}e

^{inx}

g(x) = ∑d

_{n}e

^{inx}

e

_{n}is defined as the Fourier Coefficients for (f*g) {the convolution} an is denoted by:

e

_{n}= 1/(2pi) integral from -pi to pi of (f*g)e

^{-inx}dx

Evaluate e

_{n}in terms of c

_{n}and d

_{n}

Hint: somewhere in the integral, the substitution z = x - y might be helpful.

## Homework Equations

For convolution, if C(x) = the integral from -infinity to infinity of (f(y)g(x-y))dx, the Fourier transform of C(x) is equal to the Fourier transform of f times the Fourier transform of g.

## The Attempt at a Solution

I'm really not too sure where to begin with this other than understanding the definition in the Relevant Equations section. Before this problem, all we were told was this definition. I do not see any way this is related to the Fourier series mentioned in the problem, let alone how to incorporate just the coefficients of the series into the integral.

Any help to point me in the right direction would be greatly appreciated.