Contents of Exponential Functions

f $\left(\vphantom{ t}\right.$ t $\left.\vphantom{ t}\right)$	F $\left(\vphantom{ s}\right.$ s $\left.\vphantom{ s}\right)$ = L $\left\{\vphantom{ f}\right.$ f $\left.\vphantom{ f}\right\}$ $\left(\vphantom{ s}\right.$ s $\left.\vphantom{ s}\right)$
e^at	${\dfrac{{1}}{{s-a}}}$
te^at	${\dfrac{{1}}{{\left( s-a\right) ^{2}}}}$
tⁿe^at	${\dfrac{{n!}}{{\left( s-a\right) ^{n+1}}}}$ , n a positive integer
${\dfrac{{e^{bt}-e^{at}}}{{t}}}$	ln ${\frac{{s-a}}{{s-b}}}$

f $\left(\vphantom{ t}\right.$ t $\left.\vphantom{ t}\right)$	F $\left(\vphantom{ s}\right.$ s $\left.\vphantom{ s}\right)$ = L $\left\{\vphantom{ f}\right.$ f $\left.\vphantom{ f}\right\}$ $\left(\vphantom{ s}\right.$ s $\left.\vphantom{ s}\right)$
${\dfrac{{1}}{{\sqrt{\pi t}}}}$ e^-a²/4t	${\dfrac{{e^{-a\sqrt{s}}}}{{\sqrt{s}}% }}$
${\dfrac{{a}}{{2\sqrt{\pi t^{3}}}}}$ e^-a²/4t	e^-a
${\dfrac{{e^{at}-e^{bt}}}{{a-b}}}$	${\dfrac{{1}}{{\left( s-a\right) \left( s-b\right) }}}$
${\dfrac{{ae^{at}-be^{bt}}}{{a-b}}}$	${\dfrac{{s}}{{\left( s-a\right) \left( s-b\right) }}}$