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used only for functions based on gamma, not functions with some obscure relation to gamma
13
votes
1
answer
555
views
Can a harmonic number be a rational number for non-integer rational argument?
Define harmonic numbers for a complex argument $z$ as $H_z=\frac{\Gamma'(z+1)}{\Gamma(z+1)}-\Gamma'(1)$.
For $n\in\mathbb{N}$, $H_n$ are usual harmonic numbers $\sum^n_{k=1} k^{-1}$ . They are obviou …
20
votes
3
answers
980
views
Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)...
I encountered this quantity in my calculations and tried to simplify it. Approximate numeric calculations suggested it could be zero (more precisely, it is certainly less than $10^{-4\times10^3}$ in a …