Gamma Function - 5.16 Sums

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
5.16.E1	${\displaystyle{\displaystyle\sum_{k=1}^{\infty}(-1)^{k}\psi'\left(k\right)=-\frac{\pi^{2}}{8}}}$ \sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}		sum((- 1)^(k)* diff( Psi(k), k$(1) ), k = 1..infinity) = -((Pi)^(2))/(8)	Sum[(- 1)^(k)* D[PolyGamma[k], {k, 1}], {k, 1, Infinity}, GenerateConditions->None] == -Divide[(Pi)^(2),8]	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.16.E2	${\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{1}{k}\psi'\left(k+1\right)=\zeta\left(3\right)}}$ \sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}		sum((1)/(k)*subs( temp=k + 1, diff( Psi(temp), temp$(1) ) ), k = 1..infinity) = Zeta(3)	Sum[Divide[1,k]*(D[PolyGamma[temp], {temp, 1}]/.temp-> k + 1), {k, 1, Infinity}, GenerateConditions->None] == Zeta[3]	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.16.E2	${\displaystyle{\displaystyle\zeta\left(3\right)=-\frac{1}{2}\psi''\left(1\right)}}$ \Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}		Zeta(3) = -(1)/(2)*subs( temp=1, diff( Psi(temp), temp$(2) ) )	Zeta[3] == -Divide[1,2]*(D[PolyGamma[temp], {temp, 2}]/.temp-> 1)	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 1]