#15033: Wrong limit value of expression involving gamma function
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Reporter: JGuzman | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: calculus | Resolution:
Keywords: maxima, gamma, limit | Merged in:
Authors: | Reviewers:
Report Upstream: Reported upstream. No | Work issues:
feedback yet. | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by pbruin):
After some Maxima debugging, it seems that the limit is evaluated via
`limit(g, x, inf)`, where `g` can be defined by
{{{
g: 1/sqrt(x)*exp(x*log(2*x-1)-(x-1/2)*log(x-1)-1/2)/2^x;
}}}
The fact that the two limits are equal follows from Stirling's
approximation. And in fact this limit is also calculated incorrectly. In
Maxima 5.33.0:
{{{
(%i1) g: 1/sqrt(x)*exp(x*log(2*x-1)-(x-1/2)*log(x-1)-1/2)/2^x;
x log(2 x - 1) - (x - 1/2) log(x - 1) - 1/2
%e
(%o1) ---------------------------------------------
x
sqrt(x) 2
(%i2) limit(g, x, inf);
(%o2) inf
}}}
The correct value is 1 (as it is for `f`).
Another strange (but possibly related) thing is that if you simplify `g`
to
{{{
g1: 1/sqrt(x)*exp(x*log(x-1/2)-(x-1/2)*log(x-1)-1/2);
}}}
then Maxima seems to be unable to compute the limit.
--
Ticket URL: <http://trac.sagemath.org/ticket/15033#comment:5>
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