---------- Forwarded message --------- From: Bill Gosper <billgosper@gmail.com> Date: Fri, Jul 10, 2020 at 7:32 AM Subject: diGamma sums To: Wolfram Tech Support I don't know if there's a general theory, but FindIntegerNullVector seems to crank these out reliably. Sum[PolyGamma[0, k]^2/k^2, {k, Infinity}] == (EulerGamma^2*Pi^2)/6 + (11*Pi^4)/360 - 2*EulerGamma*Zeta[3] Sum[PolyGamma[0, k]^3/k^2, {k, Infinity}] == (-(1/6))*EulerGamma^3*Pi^2 - (11*EulerGamma*Pi^4)/120 + 3*EulerGamma^2*Zeta[3] + (1/6)*Pi^2*Zeta[3] + (15*Zeta[5])/2 Sum[PolyGamma[0, k]^2/k^3, {k, Infinity}] == -((EulerGamma*Pi^4)/180) + EulerGamma^2*Zeta[3] + (1/6)*Pi^2*Zeta[3] - (3*Zeta[5])/2 Similarly for HarmonicNumber vs PolyGamma. Perhaps you should offer such results via the function ConjectureExpand.-) —Bill