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The transform of $\bm{t^n}$

\begin{eqnarray*}
\mathcal{L}[t^n](s) & = & \int_0^\infty {\rm e}^{-st} t^n {\r...
...ac{u^n}{s^{n+1}} {\rm d}u \\
& = & \frac{\Gamma(n+1)}{s^{n+1}}
\end{eqnarray*}



where $\Gamma(\alpha) := \int_0^\infty {\rm e}^{-y} y^{\alpha - 1}\,{\rm d}y$ and $u := st$.



Alexander Frolkin 2002-02-14