maxima-bounces at math.utexas.edu wrote on 11/26/2007 12:15:14 PM:
> On Nov 26, 2007 3:36 AM, Andrej Vodopivec <andrej.vodopivec at gmail.com>
wrote:
> > (%i1) gamma ((x+1)/2)/(sqrt(x)*gamma (x/2))$
> > (%i2) tlimit(%, x, inf);
> > (%o2) 1/sqrt(2)
>
> Interesting, since taylor(%i1,x,inf,0) gives an error (essential
> singularity). It seems that tlimit has other tricks up its sleeve....
>
> -s
But not enough tricks for a slightly more difficult problem:
(%i3) x * (gamma ((x+1)/2)/(sqrt(x)*gamma (x/2)) - 1/sqrt(2));
(%o3) x*(gamma((x+1)/2)/(sqrt(x)*gamma(x/2))-1/sqrt(2))
(%i4) tlimit(%,x,inf);
(%o4) limit(((x/2-1/2)!*sqrt(x))/(x/2-1)!-x/sqrt(2),x,inf)
BW