δ(ax)=1|a|δ(x)δ(−x)=δ(x)δ((x−a)(x−b))=[δ(x−a)+δ(x−a)]|a−b|(x−b))=[δ(x−a)+δ∣a−bδ(f(x))=∑jδ(x−xj)|f′(xj)| for
There seems to be a mistake here,
$$\frac{\delta(x-a) + \delta(x-b)}{|a-b|}$$
2 Matching Annotations
- Last 7 days
-
math.libretexts.org math.libretexts.org
-
-
math.libretexts.org math.libretexts.org
-
This calculation seems to be incorrect. $$\int^{\Omega}{\Omega} e^{\omega x} d\omega$$ $$= \frac{e^{i\omega x}}{i x} \bigg |^{\Omega}{-\Omega}$$ $$= \frac{e^{i x \Omega} - e^{-i x \Omega}}{i x}$$ $$= 2 \Omega \operatorname{sinc}(\Omega x) $$
-