Definition: ##f(x+k) = \exp(k \frac{d}{dx}) f(x)##(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Shift operator is useful for what?

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