Tabelle der Carson-Heaviside-Transformation

Tabelle C.2: Tabelle der Carson-Heaviside-Transformationen einiger ausgewählter Funktionen

	$f(t)$, $(t>0)$	$F\left( p \right)=p\int\limits_0^\infty {f\left( t \right)e^{-pt}dt}$
1.	$\frac{t^n}{\Gamma (n+1)}$	$\frac{1}{p^n}$
2.	$e^{-at}$	$\frac{p}{p+a}$
3.	$\sin(kt)$	$\frac{pk}{p^2+k^2}$
4.	$\cos(kt)$	$\frac{p^2}{p^2+k^2}$
5.	$e^{-at}\sin \left(kt\right)$	$\frac{pk}{\left( p+a \right)^2 + k^2}$
6.	$e^{-at}\cos \left( kt \right)$	$\frac{p \left( p+a \right)}{\left( p+a \right)^2 + k^2}$
7.	$t \sin \left( kt \right)$	$\frac{2 k p^2}{\left( p^2 + k^2 \right)^2}$
8.	$t \cos \left( kt \right)$	$\frac{p \left( p^2 - k^2 \right)}{\left( p^2 + k^2 \right)^2}$
9.	$e^{-at} {\frac{t^n}{n!}}$	$\frac{p}{\left( p+a \right)^{n+1}}$
10.	$\frac{\left ( 2 t \right)^n}{1\cdot 3\cdot 5\ldots \left( {2n-1} \right)\sqrt {\pi t}}$	$\frac{\sqrt{p}}{p^n}\;\;\;$(n ganzzahlig $>$0)
11.	${\frac{1}{\sqrt {\pi t}}}e^{-\frac{a^2}{4t}}$	$\sqrt{p}e^{-a\sqrt{p}}\;\;\;$(a$>$0)
12.	${\frac{a}{2\sqrt {\pi t^3}}}e^{-\frac{a^2}{4t}}$	$pe^{-a\sqrt p}$
13.	$J_0\left( t \right) \;\;\;$(Besselfunktion)	$\frac {p}{\sqrt{1+p^2}}$
14.	$I_0\left( t \right) \;\;\;$(Besselfunktion)	$\frac {p}{\sqrt{p^2-1}}$
15.	$\int\limits_t^\infty {{\frac{e^{-x}}{ x}}dx}$	$\ln \left( {1+p} \right)$