- #1
Jhenrique
- 685
- 4
Definition: ##f(x+k) = \exp(k \frac{d}{dx}) f(x)##
So I thought, how take advantage this definition? Maybe it be usefull in integration like is the laplace transform. So I tried to integrate the expression
##\int f(x+k) dx = \int \exp(k \frac{d}{dx}) f(x) dx ## that is an integration by parts, so is necessary to know to integrate and/or differentiate ##exp(k \frac{d}{dx})## and I don't know how do it!
I'm in the correct path?
So I thought, how take advantage this definition? Maybe it be usefull in integration like is the laplace transform. So I tried to integrate the expression
##\int f(x+k) dx = \int \exp(k \frac{d}{dx}) f(x) dx ## that is an integration by parts, so is necessary to know to integrate and/or differentiate ##exp(k \frac{d}{dx})## and I don't know how do it!
I'm in the correct path?