Why does this work (for all $a>0$). How can you prove the formula
$\lim_{L\rightarrow \infty}\int\limits_{-a^2}^{a^2} \frac{f(x) \sin(Lx)}{\pi x} dx=f(0)$
Does it work for all functions f?
Why does this work (for all $a>0$). How can you prove the formula
$\lim_{L\rightarrow \infty}\int\limits_{-a^2}^{a^2} \frac{f(x) \sin(Lx)}{\pi x} dx=f(0)$
Does it work for all functions f?