Mathematica 10.1.0 fails to compute the following limit:
Limit[Log[X]^(3/2)*(-1 - 1/Sqrt[Log[X]] + (1 + 2/Log[X]^2)^p*
(1 + 1/Sqrt[Log[X/2 + X/Log[X]^2]])),
X -> Infinity, Assumptions -> {Element[p, Reals]}]
After ten seconds or so, it simply returns the unevaluated expression even though the limit is $\frac{1}{2}\ln 2$ irrespective of the value of $p$. I'm fairly sure that this is the case because:
- I've proven it in a proof assistant (Isabelle/HOL)
- Maple outputs the correct result
- Mathematica outputs the correct result if any concrete value is substituted for $p$
Is this some kind of fundamental restriction of Mathematica regarding free variables in expressions or am I missing something here? (Someone in the ##mathematica IRC channel claimed it worked fine in his Mathematica version, so perhaps the version is relevant?)