What is $\displaystyle\frac{d^{(1/2)}}{dx^{(1/2)}}(i)$ I saw some youtube videos about half derivatives, and was curious if this has an answer.
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1Does this answer your question? What does a "half derivative" mean? – Tab1e May 18 '20 at 17:21
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Can you tell us what a "half derivative" is. And you can have half derivatives of constants. What is $\frac {d^{\frac 12}}{dx^{\frac 12}} 27$? – fleablood May 18 '20 at 17:22
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Wouldn't $\frac {d^{k}}{dx^k} c = 0$ for all $k$ and all constants $c$. $i$ is in no way a function and the fact that is imaginary does not change that it is a constant. – fleablood May 18 '20 at 17:26
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That must be a function such that its half derivative is zero. – May 18 '20 at 17:27
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2@fleablood: this is true for all integers $k\ge1$, but for $k=\frac12$ we don't know. – May 18 '20 at 17:28
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1If derivative is Riemann–Liouville then answer is: $\displaystyle\frac{d^{(1/2)}}{dx^{(1/2)}}(i)=\mathcal{L}_s^{-1}\left\sqrt{s} \left(\mathcal{L}_x[i](s)\right)\right=\frac{i}{\sqrt{\pi } \sqrt{x}}$ – Mariusz Iwaniuk May 18 '20 at 18:12