In relation to this question: Exponential of a polynomial of the differential operator
Is there an expression for $\exp(aD^n)f(x)$ similar to $\exp(aD)f(x)=f(x+a)$?
In relation to this question: Exponential of a polynomial of the differential operator
Is there an expression for $\exp(aD^n)f(x)$ similar to $\exp(aD)f(x)=f(x+a)$?