don@allegra.UUCP (12/11/83)
Let D be the operator d/dx, and consider the operator exp(D). Prove that for any continuous differentiable function, f, the following is true: exp(D) f(x) = f(x + 1)
ags@pucc-k (Seaman) (12/13/83)
More generally, if D is the operator d/dx and h is a real number, then hD is the operator h d/dx, and exp(hD) f(x) = f(x+h) Dave Seaman ..!pur-ee!pucc-k!ags
quiroz@rochester.UUCP (Cesar Quiroz) (12/13/83)
In a word : exp(D) = 1 + D + ... + (D^n)/n! + ... (as operators) so: exp(D) f(x) = f(x) + Df(x) + D^2 f(x) /2! + ...D^n f(x) / n! ... = sum [ D^i f(x) / i! * ((x+1) -x)^i ] i= 0,1,... = Taylor expansion for f around x, eval. at 1 = f(x+1) Cesar Quiroz UofR Comp Sc Dpt.