Hello Group,
This is not a burning issue, but it has me confused. If I enter
LaplaceTransform[t, t, s, GenerateConditions -> True]
MMA 10.3.1 returns
1/s^2
(with no conditions shown.) If I enter
LaplaceTransform[E^(2 t), t, s, GenerateConditions -> True]
I get back
1/(-2 + s)
also with no conditions. However, if I enter the transform definition versions,
Integrate[t Exp[ -s t], {t, 0, Infinity}]
or
Integrate[Exp[2 t] Exp[ -s t], {t, 0, Infinity}]
it gives ConditionalExpressions showing appropriate conditions, such as
ConditionalExpression[1/(-2 + s), Re[s] > 2]
Why does it do this? In the documentation for LaplaceTransform it shows an expression that does cause generation of a ConditionalExpression, so I’m wondering what makes it show ConditionalExpressions sometimes, but not always.