# Mathematica 11: Mellin transform conditions?

Consider the expression

fun = 1/(y^2-1)^a;


If I do the Mellin Transform explicitly, I get a result that involves a few conditions on the parameters a,s

Integrate[(y)^(s - 1)fun, {y, 0, Infinity}]


ConditionalExpression[ 1/2 Gamma[ 1 - a] (Gamma[a - s/2]/Gamma[1 - s/2] + ((-1)^-a Gamma[s/2])/ Gamma[1 - a + s/2]) , 2 a > Re[s] && Re[s] > 0 && a < 1]

However, if I just use the Mellin transform function, no restrictions on the parameters a,s appear:

MellinTransform[fun, y, s]


1/2 Gamma[ 1 - a] (Gamma[a - s/2]/Gamma[1 - s/2] + ((-1)^-a Gamma[s/2])/ Gamma[1 - a + s/2])

Which result should I trust? Are the restrictions really necessary, or is there maybe some analytic continuation going on which the MellinTransform function knows about while Integrate does not?

From the docs:

MellinTransform[1/(y^2 - 1)^a, y, s, GenerateConditions -> True]

ConditionalExpression[