Exponential, Logarithmic, Sine, and Cosine Integrals - 6.6 Power Series
Jump to navigation
Jump to search
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 6.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEi@{x} = \EulerConstant+\ln@@{x}+\sum_{n=1}^{\infty}\frac{x^{n}}{n!\thinspace n}}
\expintEi@{x} = \EulerConstant+\ln@@{x}+\sum_{n=1}^{\infty}\frac{x^{n}}{n!\thinspace n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0} | Error
|
ExpIntegralEi[x] == EulerGamma + Log[x]+ Sum[Divide[(x)^(n),(n)!*n], {n, 1, Infinity}, GenerateConditions->None]
|
Missing Macro Error | Failure | - | Successful [Tested: 3] |
| 6.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = -\EulerConstant-\ln@@{z}-\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{n}}{n!\thinspace n}}
\expintE@{z} = -\EulerConstant-\ln@@{z}-\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{n}}{n!\thinspace n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Ei(z) = - gamma - ln(z)- sum(((- 1)^(n)* (z)^(n))/(factorial(n)*n), n = 1..infinity)
|
ExpIntegralE[1, z] == - EulerGamma - Log[z]- Sum[Divide[(- 1)^(n)* (z)^(n),(n)!*n], {n, 1, Infinity}, GenerateConditions->None]
|
Failure | Failure | Failed [7 / 7] Result: 1.393548628+1.498247032*I
Test Values: {z = 1/2*3^(1/2)+1/2*I}
Result: .8944744989+3.773814377*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Successful [Tested: 7] |
| 6.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = -\ln@@{z}+e^{-z}\sum_{n=0}^{\infty}\frac{z^{n}}{n!}\digamma@{n+1}}
\expintE@{z} = -\ln@@{z}+e^{-z}\sum_{n=0}^{\infty}\frac{z^{n}}{n!}\digamma@{n+1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Ei(z) = - ln(z)+ exp(- z)*sum(((z)^(n))/(factorial(n))*Psi(n + 1), n = 0..infinity)
|
ExpIntegralE[1, z] == - Log[z]+ Exp[- z]*Sum[Divide[(z)^(n),(n)!]*PolyGamma[n + 1], {n, 0, Infinity}, GenerateConditions->None]
|
Failure | Failure | Failed [7 / 7] Result: 1.393548628+1.498247031*I
Test Values: {z = 1/2*3^(1/2)+1/2*I}
Result: .8944744987+3.773814376*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Successful [Tested: 7] |
| 6.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEin@{z} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}z^{n}}{n!\thinspace n}}
\expintEin@{z} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}z^{n}}{n!\thinspace n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ExpIntegralE[1, z] + Ln[z] + EulerGamma == Sum[Divide[(- 1)^(n - 1)* (z)^(n),(n)!*n], {n, 1, Infinity}, GenerateConditions->None]
|
Missing Macro Error | Failure | - | Failed [7 / 7]
Result: Plus[Complex[0.0, -0.5235987755982988], Ln[Complex[0.8660254037844387, 0.49999999999999994]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[Complex[0.0, -2.0943951023931953], Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 6.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinint@{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{(2n+1)!(2n+1)}}
\sinint@{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{(2n+1)!(2n+1)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Si(z) = sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(2*n + 1)*(2*n + 1)), n = 0..infinity)
|
SinIntegral[z] == Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(2*n + 1)!*(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]
|
Successful | Successful | - | Successful [Tested: 7] |
| 6.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosint@{z} = \EulerConstant+\ln@@{z}+\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{2n}}{(2n)!(2n)}}
\cosint@{z} = \EulerConstant+\ln@@{z}+\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{2n}}{(2n)!(2n)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Ci(z) = gamma + ln(z)+ sum(((- 1)^(n)* (z)^(2*n))/(factorial(2*n)*(2*n)), n = 1..infinity)
|
CosIntegral[z] == EulerGamma + Log[z]+ Sum[Divide[(- 1)^(n)* (z)^(2*n),(2*n)!*(2*n)], {n, 1, Infinity}, GenerateConditions->None]
|
Successful | Successful | - | Successful [Tested: 7] |