0
$\begingroup$

I have a question if you don't mind. I have the following quotient operator: $$\frac{1}{e^{d/dx}(f(x))}$$ Where $f$ is a smooth function on $R$. I would like to get rid of the denominator. IS there any formula that i Can found in your papers or other references and use it for this case? Thanks and best regards.

$\endgroup$

1 Answer 1

4
$\begingroup$

The exponentiated operator shifts $f$ by one unit in $x$, i.e., $$ \frac{1}{e^{d/dx} (f(x))} = \frac{1}{f(x+1)} $$ It's not quite clear what is desired by "getting rid of the denominator" - the result just happens to be the reciprocal of $f$. You could define $g=1/f$ and have an expression without a fraction.

$\endgroup$
2
  • $\begingroup$ Where did you found this formula is this the developement of Taylor? $\endgroup$ Jun 22, 2021 at 14:03
  • $\begingroup$ The shift operator is described here, en.wikipedia.org/wiki/Shift_operator - you can also find some references there if you want to cite something. $\endgroup$ Jun 22, 2021 at 15:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.