Zeta and Related Functions - 25.16 Mathematical Applications
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 25.16.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\Riemannzeta@{1-2a} = -\frac{\BernoullinumberB{2a}}{4a}}
\frac{1}{2}\Riemannzeta@{1-2a} = -\frac{\BernoullinumberB{2a}}{4a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2)*Zeta(1 - 2*a) = -(bernoulli(2*a))/(4*a)
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Divide[1,2]*Zeta[1 - 2*a] == -Divide[BernoulliB[2*a],4*a]
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Failure | Failure | Successful [Tested: 1] | Successful [Tested: 1] |
| 25.16.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}\left(\frac{h(n)}{n}\right)^{2} = \frac{17}{4}\Riemannzeta@{4}}
\sum_{n=1}^{\infty}\left(\frac{h(n)}{n}\right)^{2} = \frac{17}{4}\Riemannzeta@{4} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(((h(n))/(n))^(2), n = 1..infinity) = (17)/(4)*Zeta(4)
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Sum[(Divide[h[n],n])^(2), {n, 1, Infinity}, GenerateConditions->None] == Divide[17,4]*Zeta[4]
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Failure | Failure | Failed [10 / 10] Result: Float(infinity)+Float(infinity)*I
Test Values: {h = 1/2*3^(1/2)+1/2*I}
Result: Float(infinity)+Float(infinity)*I
Test Values: {h = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Failed [10 / 10]
Result: Plus[-4.599873743272337, NSum[Power[E, Times[Complex[0, Rational[1, 3]], Pi]]
Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[-4.599873743272337, NSum[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]]
Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[h, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 25.16.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{r=1}^{\infty}\sum_{k=1}^{r}\frac{1}{rk(r+k)} = \frac{5}{4}\Riemannzeta@{3}}
\sum_{r=1}^{\infty}\sum_{k=1}^{r}\frac{1}{rk(r+k)} = \frac{5}{4}\Riemannzeta@{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(sum((1)/(r*k*(r + k)), k = 1..r), r = 1..infinity) = (5)/(4)*Zeta(3)
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Sum[Sum[Divide[1,r*k*(r + k)], {k, 1, r}, GenerateConditions->None], {r, 1, Infinity}, GenerateConditions->None] == Divide[5,4]*Zeta[3]
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Failure | Aborted | Error | Successful [Tested: 1] |