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$\psi(2,1/6),\psi(4,1/6)$ in terms of zeta and pi only and another closed form for zeta
Let $\psi(n,x)$ denote the polygamma function.
In this answer Lucia gave linear relations for $\psi(m,1/3),\psi(m,1/6),\zeta(m+1)$.
The computer managed to find closed form for $\psi(2,1/6)$ and $\...
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