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For what values of $\nu$ does the Riemann-Liouville differintegral $_{-\infty}D_{z}^\nu$ of the digamma function $\psi(z)=\frac{\Gamma'(z)}{\Gamma(z)}$ exist, with $c=-\infty$? All I've got so far is that the derivatives exist, i.e. the differintegrals when $\mathrm{Re}(\nu)>0 $.

Many thanks for any help with this!

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    Have you by any chance seen [the paper by Moll and Espinosa](http://www.tandfonline.com/doi/abs/10.1080/10652460310001600573)? That might give you something to start with... still, the poles of the polygamma functions in the left half-plane has me skeptical that the beasts are well-defined for noninteger $\nu$ and lower limit $-\infty$...2012-11-25

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