- #1
VinnyCee
- 489
- 0
I am not sure I am doing this correctly, so here it is.
Problem:
Find the Fourier Series
[tex]f(s)\,=\,\left\{\begin{array}{ccc}x^2&-\pi\,<\,x\,<\,0\\0 &0\,<x\,<\,\pi \\}\end{array}\right[/tex]
Answer(supposedly):
[tex]a_0\,=\,\frac{\pi^3}{3}[/tex]
[tex]a_n\,=\,-\frac{2}{n^2}[/tex]
[tex]b_n\,=\,\frac{4\,-\,n^2\,\pi^2}{n^3\,\pi}[/tex]
Does that look right? If so, where do I gofrom here?
[tex]f(s)\,\approx\,\frac{\pi^3}{3}\,+\,\sum_{n\,=\,1}^{\infty}\,\left[-\frac{2}{n^2}\,cos(n\,x)\,+\,\frac{4\,-\,n^2\,\pi^2}{n^3\,\pi}\,sin(n\,x)\right][/tex]
Is this the final answer?
Problem:
Find the Fourier Series
[tex]f(s)\,=\,\left\{\begin{array}{ccc}x^2&-\pi\,<\,x\,<\,0\\0 &0\,<x\,<\,\pi \\}\end{array}\right[/tex]
Answer(supposedly):
[tex]a_0\,=\,\frac{\pi^3}{3}[/tex]
[tex]a_n\,=\,-\frac{2}{n^2}[/tex]
[tex]b_n\,=\,\frac{4\,-\,n^2\,\pi^2}{n^3\,\pi}[/tex]
Does that look right? If so, where do I gofrom here?
[tex]f(s)\,\approx\,\frac{\pi^3}{3}\,+\,\sum_{n\,=\,1}^{\infty}\,\left[-\frac{2}{n^2}\,cos(n\,x)\,+\,\frac{4\,-\,n^2\,\pi^2}{n^3\,\pi}\,sin(n\,x)\right][/tex]
Is this the final answer?