# Fourier Series Odd function

1. Mar 24, 2010

### mbud

1. The problem statement, all variables and given/known data

Determine a general Fourier series representation for f(x) = x^3 -1<x<1

2. Relevant equations

3. The attempt at a solution

May seem like a stupid Q, but would i have to calculate a0, an, bn or since i know that x^3 is an odd function, could jump straight into calculating the Fourier sine series for odd functions. Would that give me a general representation?

Last edited: Mar 24, 2010
2. Mar 24, 2010

### vishal007win

if you calculate all the terms initially assuming the complete Fourier representation you will find that coefficients associated with the even terms will go to zero.
so its more like using a known result.

3. Mar 24, 2010

### CompuChip

Yes, you can restrict yourself to sines.

If you want you can explicitly check it, with an argument along the lines of
$$\int_{-1}^1 \cos(x) x^3 dx = \int_{-1}^0 \cos(x) x^3 dx + \int_0^1 \cos(x) x^3 dx = \int_0^1 \cos(-x) (-x)^3 dx + \int_0^1 \cos(x) x^3 dx = 0$$
because cos(-x) (-x)3 = - cos(x) x3

4. Mar 24, 2010

thanks.