f(x) = xsin(px)
to calculate the fourier series, I am struggling.. do I need to distinguish between when p = n?
I am really struggling with the integration of this.. could somebody please show me how I would go about it? many thanks
f(x) = xsin(px)
to calculate the fourier series, I am struggling.. do I need to distinguish between when p = n?
I am really struggling with the integration of this.. could somebody please show me how I would go about it? many thanks
Here's what I got
$\displaystyle a_0 = \frac{1}{\pi} \int_{- \pi}^{\pi} x \sin p x\, dx = - \frac{2 (-1)^p}{p}$
$\displaystyle a_n = \frac{1}{\pi} \int_{- \pi}^{\pi} x \sin p x \cos nx\, dx = - \frac{2 p}{p^2 -n^2}\,(-1)^{p+n}\;\;\;n \ne p$
$\displaystyle a_n = - \frac{1}{2p},\;\;\;n = p$
The series
$\displaystyle \frac{a_0}{2} + \sum_{i=1}^{\infty} a_n \cos nx$