Definite Integral to Infinity of Power of x by Exponential of -a x^2

Theorem

 * $\ds \int_0^\infty x^m e^{-a x^2} \rd x = \frac {\map \Gamma {\paren {m + 1}/2} } {2 a^{\paren {m + 1}/2} }$

where $m$ and $a$ are real numbers with $m > -1$ and $a > 0$.