File:MathematicaBug01Fragment.jpg

Screenshot of the Mathematica frame, that shows bug in the Mathematica software. The two outputs contradict each other.

Mathematica source
The image shown in the screenshot above is generated with the two lines below:

Series[BesselJ[0, Sqrt[x]] Sqrt[Pi x^(5/2)/2]/(1+x), {x,Infinity,2}]

Series[BesselJ[0, x] Sqrt[Pi/2] x^(5/2)/(1+x^2), {x,Infinity,4}]