Gamma Function - 5.16 Sums
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 5.16.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}}
\sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((- 1)^(k)* diff( Psi(k), k$(1) ), k = 1..infinity) = -((Pi)^(2))/(8)
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Sum[(- 1)^(k)* D[PolyGamma[k], {k, 1}], {k, 1, Infinity}, GenerateConditions->None] == -Divide[(Pi)^(2),8]
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Failure | Successful | Successful [Tested: 0] | Successful [Tested: 1] |
| 5.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}}
\sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((1)/(k)*subs( temp=k + 1, diff( Psi(temp), temp$(1) ) ), k = 1..infinity) = Zeta(3)
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Sum[Divide[1,k]*(D[PolyGamma[temp], {temp, 1}]/.temp-> k + 1), {k, 1, Infinity}, GenerateConditions->None] == Zeta[3]
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Failure | Successful | Successful [Tested: 0] | Successful [Tested: 1] |
| 5.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}}
\Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Zeta(3) = -(1)/(2)*subs( temp=1, diff( Psi(temp), temp$(2) ) )
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Zeta[3] == -Divide[1,2]*(D[PolyGamma[temp], {temp, 2}]/.temp-> 1)
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Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 1] |