- #1
jusy1
- 1
- 0
Hi everybody
I was trying to prove that \int_{-\infty}^{\infty}e^{\imath (k - k') x}dx = 2\pi\delta(k-k') by solving \lim_{L\rightarrow \infty} \int_{-L}^{L}e^{\imath (k - k') x}dx
knowing that \delta(x)=\lim_{g\rightarrow \infty}\frac{\sin(gx)}{\pi x}
But is there a way of proving this result using complex analysis?
I was trying to prove that \int_{-\infty}^{\infty}e^{\imath (k - k') x}dx = 2\pi\delta(k-k') by solving \lim_{L\rightarrow \infty} \int_{-L}^{L}e^{\imath (k - k') x}dx
knowing that \delta(x)=\lim_{g\rightarrow \infty}\frac{\sin(gx)}{\pi x}
But is there a way of proving this result using complex analysis?
