I am trying to define a function (an operator) that "integrates then translates" a function. More specifically, for an input f[x], I want to integrate it as \int_0^x f[t] dt, then translate this function by one unit to the left.
I tried the following code:
Integrate[#, {t, 0, x}, Assumptions -> x \[Element] Reals], x]) /. x -> t & This code works on many elementary functions with the Nest command. For example,
NestList[S[x], Exp[t], 2] returns
{E^t, -1 + E^(1 + t), -1 + E (-1 + E^(1 + t)) - t} (where E is the usual e). However, for a more exotic input function like Exp[Exp[t]], Mathematica gives me a conditional expression:
{E^E^t, ConditionalExpression[-ExpIntegralEi[1] + ExpIntegralEi[E^(1 + t)], t > -1]} I attempted adding assumptions that the variables x and t are real in my definition of S[x_], but I have not been able to work around my issue.
I know there is no closed form for the integral of e^e^x; ultimately, I just want to plot the iterates of a given starting function. Is there a different way to define this operator at the beginning so that its iterates are able to be plotted?
