Exponential, Logarithmic, Sine, and Cosine Integrals - 6.4 Analytic Continuation
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 6.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = \expintEin@{z}-\Ln@@{z}-\EulerConstant}
\expintE@{z} = \expintEin@{z}-\Ln@@{z}-\EulerConstant |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ExpIntegralE[1, z] == ExpIntegralE[1, z] + Ln[z] + EulerGamma - Log[z]- EulerGamma
|
Missing Macro Error | Failure | - | Failed [7 / 7]
Result: Plus[Complex[0.0, 0.5235987755982988], Times[-1.0, 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], Times[-1.0, Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 6.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{ze^{2m\pi i}} = \expintE@{z}-2m\pi i}
\expintE@{ze^{2m\pi i}} = \expintE@{z}-2m\pi i |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Ei(z*exp(2*m*Pi*I)) = Ei(z)- 2*m*Pi*I
|
ExpIntegralE[1, z*Exp[2*m*Pi*I]] == ExpIntegralE[1, z]- 2*m*Pi*I
|
Failure | Failure | Failed [21 / 21] Result: -.1e-8+6.283185310*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, m = 3}
Result: -.6e-8+12.56637063*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 2, m = 3}
... skip entries to safe data |
Failed [7 / 7]
Result: Complex[0.0, 18.84955592153876]
Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[0.0, 18.84955592153876]
Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 6.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{ze^{+\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant-\pi i}
\expintE@{ze^{+\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant-\pi i |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}| \leq \pi} | Error
|
ExpIntegralE[1, z*Exp[+ Pi*I]] == ExpIntegralE[1, - z] + Ln[- z] + EulerGamma - Log[z]- EulerGamma - Pi*I
|
Missing Macro Error | Failure | - | Failed [7 / 7]
Result: Plus[Complex[0.0, 3.6651914291880923], Times[-1.0, Ln[Complex[-0.8660254037844387, -0.49999999999999994]]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[Complex[0.0, 5.235987755982989], Times[-1.0, Ln[Complex[0.4999999999999998, -0.8660254037844387]]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 6.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{ze^{-\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant+\pi i}
\expintE@{ze^{-\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant+\pi i |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}| \leq \pi} | Error
|
ExpIntegralE[1, z*Exp[- Pi*I]] == ExpIntegralE[1, - z] + Ln[- z] + EulerGamma - Log[z]- EulerGamma + Pi*I
|
Missing Macro Error | Failure | - | Failed [7 / 7]
Result: Plus[Complex[0.0, -2.6179938779914944], Times[-1.0, Ln[Complex[-0.8660254037844387, -0.49999999999999994]]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[Complex[0.0, -1.0471975511965976], Times[-1.0, Ln[Complex[0.4999999999999998, -0.8660254037844387]]]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 6.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosint@{ze^{+\pi i}} = +\pi i+\cosint@{z}}
\cosint@{ze^{+\pi i}} = +\pi i+\cosint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Ci(z*exp(+ Pi*I)) = + Pi*I + Ci(z)
|
CosIntegral[z*Exp[+ Pi*I]] == + Pi*I + CosIntegral[z]
|
Failure | Failure | Failed [2 / 7] Result: 0.-6.283185308*I
Test Values: {z = 1/2*3^(1/2)+1/2*I}
Result: 0.-6.283185308*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}
|
Failed [2 / 7]
Result: Complex[0.0, -6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[0.0, -6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
|
| 6.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosint@{ze^{-\pi i}} = -\pi i+\cosint@{z}}
\cosint@{ze^{-\pi i}} = -\pi i+\cosint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Ci(z*exp(- Pi*I)) = - Pi*I + Ci(z)
|
CosIntegral[z*Exp[- Pi*I]] == - Pi*I + CosIntegral[z]
|
Failure | Failure | Failed [5 / 7] Result: 0.+6.283185308*I
Test Values: {z = 1/2-1/2*I*3^(1/2)}
Result: 0.+6.283185308*I
Test Values: {z = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data |
Failed [5 / 7]
Result: Complex[0.0, 6.283185307179585]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
Result: Complex[0.0, 6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
... skip entries to safe data |
| 6.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coshint@{ze^{+\pi i}} = +\pi i+\coshint@{z}}
\coshint@{ze^{+\pi i}} = +\pi i+\coshint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Chi(z*exp(+ Pi*I)) = + Pi*I + Chi(z)
|
CoshIntegral[z*Exp[+ Pi*I]] == + Pi*I + CoshIntegral[z]
|
Failure | Failure | Failed [2 / 7] Result: 0.-6.283185308*I
Test Values: {z = 1/2*3^(1/2)+1/2*I}
Result: 0.-6.283185307*I
Test Values: {z = -1/2+1/2*I*3^(1/2)}
|
Failed [2 / 7]
Result: Complex[0.0, -6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[0.0, -6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
|
| 6.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coshint@{ze^{-\pi i}} = -\pi i+\coshint@{z}}
\coshint@{ze^{-\pi i}} = -\pi i+\coshint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Chi(z*exp(- Pi*I)) = - Pi*I + Chi(z)
|
CoshIntegral[z*Exp[- Pi*I]] == - Pi*I + CoshIntegral[z]
|
Failure | Failure | Failed [5 / 7] Result: 0.+6.283185307*I
Test Values: {z = 1/2-1/2*I*3^(1/2)}
Result: 0.+6.283185308*I
Test Values: {z = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data |
Failed [5 / 7]
Result: Complex[0.0, 6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
Result: Complex[0.0, 6.283185307179586]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
... skip entries to safe data |