# Thread: PDE-fourier sine series (help!!!)

1. ## PDE-fourier sine series (help!!!)

do i use the bessel's equation to solve this problem?any help will be appreciated thanks.

2. Originally Posted by canuhelp

do i use the bessel's equation to solve this problem?any help will be appreciated thanks.
As the question says, use a Fourier Sine series. Here

$
f(x) = \frac{\pi-x}{2} = \sum_{n=1}^{\infty} a_n \sin nx
$

where $a_n = \frac{2}{\pi} \int_0^{\pi} f(x) \sin nx\,dx = \frac{1}{n }$

so

$
\frac{\pi-x}{2} = \sum_{n=1}^{\infty} \frac{\sin nx}{n}
$

Now sub. in $x = \frac{\pi}{2}$