I was slightly surprised by the following result:
PossibleZeroQ[Gamma[a + b]/Gamma[a] - Pochhammer[a, b]] (* Out: False *)
PossibleZeroQ[Gamma[a + b]/Gamma[a] - Pochhammer[a, b] // FunctionExpand] (* Out: True *)
I had the wrong impression (maybe from the name) that
PossibleZeroQ would be more likely to err by giving false positives than false negatives. I would think that numerical tests would indeed confirm that these expressions are the same. I guess the problem comes from the poles/zero's of the
Gamma function. Or should I really be careful with
FunctionExpand and does it really give possibly false results?
P.S. I came across this in a more practical situation where the equality of two expressions was not easy to see by hand, but simplified it to this core oddity.