I posted a problem and my solution to it. I got several fine responses and now I have the right solution. I am wondering, what is the level of difficulty of the question? math.stackexchange.com/questions/2366451/…
I've got a power series of the form $\sum_{n=0}^\infty \frac{\Gamma(1/4+n/2)}{n!} (-x)^n$
It might look a little strange, but this has infinite radius of convergence per the ratio test so everything would seem to be fine.
However, Mathematica yields some weird behavior on the negative real axis.
In particular, if you plug $x=-1$ directly into the above and sum, Mathematica yields roughly 5.5227.
But you can instead allow Mathematica to compute the sum as a function of $x$, do a FullSimplify to make things look nicer, and only then plug in $x=-1$. If you do that, you get 2.73685i as the output!
Weirder still, this only happens if you do FullSimplify and does not happen if you only do Simplify.
