Exponential, Logarithmic, Sine, and Cosine Integrals - 6.15 Sums
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 6.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}\cosint@{\pi n} = \tfrac{1}{2}(\ln@@{2}-\EulerConstant)}
\sum_{n=1}^{\infty}\cosint@{\pi n} = \tfrac{1}{2}(\ln@@{2}-\EulerConstant) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(Ci(Pi*n), n = 1..infinity) = (1)/(2)*(ln(2)- gamma)
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Sum[CosIntegral[Pi*n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[2]- EulerGamma)
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Failure | Failure | Successful [Tested: 0] | Failed [1 / 1]
Result: Plus[-0.05796575782920621, NSum[CosIntegral[Times[n, Pi]]
Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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| 6.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}\frac{\shiftsinint@{\pi n}}{n} = \tfrac{1}{2}\pi(\ln@@{\pi}-1)}
\sum_{n=1}^{\infty}\frac{\shiftsinint@{\pi n}}{n} = \tfrac{1}{2}\pi(\ln@@{\pi}-1) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((Ssi(Pi*n))/(n), n = 1..infinity) = (1)/(2)*Pi*(ln(Pi)- 1)
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Sum[Divide[SinIntegral[Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*(Log[Pi]- 1)
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Failure | Failure | Successful [Tested: 0] | Failed [1 / 1]
Result: Plus[-0.22734117306968246, NSum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]]
Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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| 6.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}(-1)^{n}\cosint@{2\pi n} = 1-\ln@@{2}-\tfrac{1}{2}\EulerConstant}
\sum_{n=1}^{\infty}(-1)^{n}\cosint@{2\pi n} = 1-\ln@@{2}-\tfrac{1}{2}\EulerConstant |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((- 1)^(n)* Ci(2*Pi*n), n = 1..infinity) = 1 - ln(2)-(1)/(2)*gamma
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Sum[(- 1)^(n)* CosIntegral[2*Pi*n], {n, 1, Infinity}, GenerateConditions->None] == 1 - Log[2]-Divide[1,2]*EulerGamma
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Failure | Failure | Successful [Tested: 0] | Failed [1 / 1]
Result: Plus[-0.018244986989288337, NSum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]]
Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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| 6.15.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}(-1)^{n}\frac{\shiftsinint@{2\pi n}}{n} = \pi(\tfrac{3}{2}\ln@@{2}-1)}
\sum_{n=1}^{\infty}(-1)^{n}\frac{\shiftsinint@{2\pi n}}{n} = \pi(\tfrac{3}{2}\ln@@{2}-1) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((- 1)^(n)*(Ssi(2*Pi*n))/(n), n = 1..infinity) = Pi*((3)/(2)*ln(2)- 1)
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Sum[(- 1)^(n)*Divide[SinIntegral[2*Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Pi*(Divide[3,2]*Log[2]- 1)
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Failure | Failure | Successful [Tested: 0] | Failed [1 / 1]
Result: Plus[-0.12478648186560967, NSum[Times[Power[-1, n], Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[2, n, Pi]]]]
Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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