I would like to find the range of the function below, but only for values of $a$ strictly greater than zero.
v[a_]=-a*Log[1-(a - a E^(-1 - 1/a + ProductLog[E^(1 + 1/a)]))/a]
In other words: what is the range of $v(a)$, for/conditional on $a>0$ (reals).
I have tried this: (ie without restricting)
FunctionRange[v[a], a, y], but the computation time is too long, I can't manage to get an output.
I also have tried to define the $v(a)$ function over the domain that interests me using this:
v[a_ /; 0 < a] := -a*Log[1-(a - a E^(-1 - 1/a + ProductLog[E^(1 + 1/a)]))/a](solution found here), and then
FunctionRange[v[a], a, y], but the computation time seems to bee stil too long. Probably due to the fact that my restricted definition doesn't seem to have worked: even in that case,
FunctionDomain[v[a],a]returns $a≠0$ (instead of $a>0$ as I would have expected since it is what I defined in the first place).
- This doesn't seem to work either:
Assuming[a>0,FunctionRange[v[a], a, y]].