Limit with gamma function gives incorrect answer

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Limit with gamma function gives incorrect answer Ed Scheinerman 8/6/13 9:01 PM
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
Re: Limit with gamma function gives incorrect answer kcrisman 8/7/13 6:35 AM


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.
Re: [sage-support] Re: Limit with gamma function gives incorrect answer Jose Guzman 8/11/13 1:56 AM
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/