matematikuvol
- 190
- 0
Homework Statement
Find Fourier transform of function
f(x)=\frac{1}{x^2+a^2}, a>0
Homework Equations
\mathcal{F}[\frac{1}{x^2+a^2}]=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}\frac{e^{-ikx}dx}{x^2+a^2}
The Attempt at a Solution
Two different case
k>0
and
k<0
How to solve integral
\mathcal{F}[\frac{1}{x^2+a^2}]=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}\frac{e^{-ikx}dx}{x^2+a^2}
Probably using complex analysis?! I forget this. I have two poles ia and -ia. How to integrate this? Is there some other method without using complex analysis?