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I want to evaluate the half derivative function of $ 1/t $

by induction i get that for every 's' then $D_{x}^{s} \frac{1}{t}=\frac{\Gamma(s+1)(-1)^{s}}{t^{s+1}} $

however if i use the formulae from mathworld i get $ D_{x}^{s}\frac{1}{t}=\frac{\Gamma (0)}{t^{s+1}} $

which is a nonsense since $ \Gamma (0) = \infty $

then which formula is correct ? , also for real 's' can i use $ (-1)^{s}=cos(\pi s) $

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S=1/2 so gamma is... and check your generalized power rule. –  user60675 Sep 6 '13 at 20:10
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