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let $D_{\mathbb N}$ be the standard "n-th derivative" function

is it possible to make a continuation of $D_{\mathbb N}$ to non integer values?

i mean a function $D_{\mathbb R}$ such that $D_{\mathbb R}(x,f)=D_{\mathbb N}(n,f)$ for all $x=n\in\mathbb N$

it should be something relevant, linear interpolation usually doesn't make any sense.

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closed as no longer relevant by Qfwfq, Bill Johnson, Ryan Budney, Andrés E. Caicedo, Andy Putman Jan 23 '12 at 3:20

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up vote 5 down vote accepted

I think you are looking for something like this:

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that's exactly what i was thinking about! i never knew such thing existed. thanks a lot – alberto.bosia Jan 22 '12 at 9:22

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