I want to integrate the function below analytically, so that later on I can use the result for numerical calculations. But it seems Mathematica can not handle it the way I express it. However, if I change the argument of the Bessel function from $s^{1/2}$ to $s$, then Mathematica handles it easily.
I tried to evaluate
int1 =
Integrate[BesselK[1, s^(1/2)/T], {s, 4 mX^2, Infinity},
GenerateConditions -> False]
and got this output:
Integrate[BesselK[1, Sqrt[s]/T], {s, 4 mX^2, Infinity}, GenerateConditions -> False]
But after changing the argument of the Bessel function from $s^{1/2 }$ to $s$:
Integrate[BesselK[1, s/T], {s, 4 mX^2, Infinity}, GenerateConditions -> False]
I got this output:
BesselK[0, (4 Sqrt[1/T^2])/Sqrt[1/mX^4]]/Sqrt[1/T^2]
which I can further use for numerical evaluation.
I need some suggestions.