Contents of Powers

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 $\left.\vphantom{ s}\right)$
1	${\dfrac{{1}}{{s}}}$
t	${\dfrac{{1}}{{s^{2}}}}$
tⁿ	${\dfrac{{n!}}{{s^{n+1}}}}$ , n a positive integer
t^-1/2	$\sqrt{{\dfrac{\pi }{s}}}$
t^1/2	${\dfrac{{\sqrt{\pi }}}{{2s^{3/2}}}}$
t^α	${\dfrac{{\Gamma \left( \alpha +1\right) }}{{s^{\alpha +1}}}}$ , α > - 1