I think I've found a minor error in the maxima integration routines.
Maxima 5.23.2 http://maxima.sourceforge.net
using Lisp SBCL 1.0.40-1.fc14
(%i1) f(x):=x^(2*n)*exp(-(x/x0)^2);
2 n x 2
(%o1) f(x) := x exp(- (--) )
x0
(%i2) integrate(f(x),x,-inf,inf);
Is 2 n + 1 positive, negative, or zero?
p;
Is 2 n an integer?
y;
(%o2) 0
The result should be zero only if 2*n is odd. If we declare n to be an
integer, the correct result is produced.
(%i3) declare(n,integer);
(%o3) done
(%i4) integrate(f(x),x,-inf,inf);
Is 2 n + 1 positive, negative, or zero?
p;
Is x0 positive or negative?
p;
2 n + 1 2 n + 1
(%o4) gamma(-------) x0
2
--
Frazer