5.16: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/5.16.E1 5.16.E1] || [[Item:Q2178|<math>\sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(k)* diff( Psi(k), k$(1) ), k = 1..infinity) = -((Pi)^(2))/(8)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(k)* D[PolyGamma[k], {k, 1}], {k, 1, Infinity}, GenerateConditions->None] == -Divide[(Pi)^(2),8]</syntaxhighlight> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
| [https://dlmf.nist.gov/5.16.E1 5.16.E1] || <math qid="Q2178">\sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(k)* diff( Psi(k), k$(1) ), k = 1..infinity) = -((Pi)^(2))/(8)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(k)* D[PolyGamma[k], {k, 1}], {k, 1, Infinity}, GenerateConditions->None] == -Divide[(Pi)^(2),8]</syntaxhighlight> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
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| [https://dlmf.nist.gov/5.16.E2 5.16.E2] || [[Item:Q2179|<math>\sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((1)/(k)*subs( temp=k + 1, diff( Psi(temp), temp$(1) ) ), k = 1..infinity) = Zeta(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[1,k]*(D[PolyGamma[temp], {temp, 1}]/.temp-> k + 1), {k, 1, Infinity}, GenerateConditions->None] == Zeta[3]</syntaxhighlight> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
| [https://dlmf.nist.gov/5.16.E2 5.16.E2] || <math qid="Q2179">\sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((1)/(k)*subs( temp=k + 1, diff( Psi(temp), temp$(1) ) ), k = 1..infinity) = Zeta(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[1,k]*(D[PolyGamma[temp], {temp, 1}]/.temp-> k + 1), {k, 1, Infinity}, GenerateConditions->None] == Zeta[3]</syntaxhighlight> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
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| [https://dlmf.nist.gov/5.16.E2 5.16.E2] || [[Item:Q2179|<math>\Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Zeta(3) = -(1)/(2)*subs( temp=1, diff( Psi(temp), temp$(2) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Zeta[3] == -Divide[1,2]*(D[PolyGamma[temp], {temp, 2}]/.temp-> 1)</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 1]
| [https://dlmf.nist.gov/5.16.E2 5.16.E2] || <math qid="Q2179">\Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Zeta(3) = -(1)/(2)*subs( temp=1, diff( Psi(temp), temp$(2) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>Zeta[3] == -Divide[1,2]*(D[PolyGamma[temp], {temp, 2}]/.temp-> 1)</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 1]
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Latest revision as of 11:13, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
5.16.E1 ∑ k = 1 ∞ ( - 1 ) k ⁢ ψ ′ ⁡ ( k ) = - π 2 8 superscript subscript 𝑘 1 superscript 1 𝑘 diffop digamma 1 𝑘 superscript 𝜋 2 8 {\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 ∑ k = 1 ∞ 1 k ⁢ ψ ′ ⁡ ( k + 1 ) = ζ ⁡ ( 3 ) superscript subscript 𝑘 1 1 𝑘 diffop digamma 1 𝑘 1 Riemann-zeta 3 {\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 ζ ⁡ ( 3 ) = - 1 2 ⁢ ψ ′′ ⁡ ( 1 ) Riemann-zeta 3 1 2 diffop digamma 2 1 {\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]
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