Limit with gamma function gives incorrect answer

[Ed Scheinerman]

When I try this:

sage: y = gamma(x+1/2)/gamma(x)/sqrt(x)

sage: limit(y,x=oo)

0

sage: plot(y,x,1,50)

I observe that the limit appears to be 1, not 0. 

Indeed, Mathematica confirms:

In[1]:= y = Gamma[x + 1/2]/(Gamma[x]*Sqrt[x])

Out[1]= Gamma[1/2 + x]/(Sqrt[x] Gamma[x])

In[2]:= Limit[y, x -> Infinity]

Out[2]= 1

[kcrisman]

On Wednesday, August 7, 2013 12:01:49 AM UTC-4, Ed Scheinerman wrote:

When I try this:

sage: y = gamma(x+1/2)/gamma(x)/sqrt(x)

sage: limit(y,x=oo)

0

sage: plot(y,x,1,50)

I observe that the limit appears to be 1, not 0. 

This is how it happens in Maxima.

(%i2) y:gamma(x+1/2)/(sqrt(x)*gamma(x));

                                           1

                                 gamma(x + -)

                                           2

(%o2)                          ----------------

                               sqrt(x) gamma(x)

(%i3) limit(y,x,0);

(%o3)                                  0

I've reported this at https://sourceforge.net/p/maxima/bugs/2621/ - if someone can open a Sage ticket for this, it would be helpful, as I don't have tons of internet time right now.

[Jose Guzman]

Reported in http://trac.sagemath.org/ticket/15033#ticket

#15033: Wrong limit value of expression involving gamma function


--
Jose Guzman
http://www.ist.ac.at/~jguzman/