Results of Exponential, Logarithmic, Sine, and Cosine Integrals

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DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
6.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = \int_{z}^{\infty}\frac{e^{-t}}{t}\diff{t}} Ei(z) = int((exp(- t))/(t), t = z..infinity) ExpIntegralE[1, z] == Integrate[Divide[Exp[- t],t], {t, z, Infinity}, GenerateConditions->None] Failure Failure
Failed [7 / 7]
7/7]: [[1.393548628+1.498247032*I <- {z = 1/2*3^(1/2)+1/2*I}
.8944744989+3.773814377*I <- {z = -1/2+1/2*I*3^(1/2)}
 Successful [Tested: 7]
6.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = e^{-z}\int_{0}^{\infty}\frac{e^{-t}}{t+z}\diff{t}} Ei(z) = exp(- z)*int((exp(- t))/(t + z), t = 0..infinity) ExpIntegralE[1, z] == Exp[- z]*Integrate[Divide[Exp[- t],t + z], {t, 0, Infinity}, GenerateConditions->None] Failure Failure
Failed [7 / 7]
7/7]: [[1.393548628+1.498247032*I <- {z = 1/2*3^(1/2)+1/2*I}
.8944744989+3.773814377*I <- {z = -1/2+1/2*I*3^(1/2)}
 Successful [Tested: 7]
6.2.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEin@{z} = \int_{0}^{z}\frac{1-e^{-t}}{t}\diff{t}} Error ExpIntegralE[1, z] + Ln[z] + EulerGamma == Integrate[Divide[1 - Exp[- t],t], {t, 0, z}, GenerateConditions->None] Missing Macro Error Failure -
Failed [7 / 7]
{Plus[Complex[0.0, -0.5235987755982988], Ln[Complex[0.8660254037844387, 0.49999999999999994]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.0, -2.0943951023931953], Ln[Complex[-0.4999999999999998, 0.8660254037844387]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
6.2.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = \expintEin@{z}-\ln@@{z}-\EulerConstant} Error ExpIntegralE[1, z] == ExpIntegralE[1, z] + Ln[z] + EulerGamma - Log[z]- EulerGamma Missing Macro Error Failure -
Failed [7 / 7]
{Plus[Complex[0.0, 0.5235987755982988], Times[-1.0, Ln[Complex[0.8660254037844387, 0.49999999999999994]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.0, 2.0943951023931953], Times[-1.0, Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
6.2.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEi@{-x} = -\int_{x}^{\infty}\frac{e^{-t}}{t}\diff{t}} Error ExpIntegralEi[- x] == - Integrate[Divide[Exp[- t],t], {t, x, Infinity}, GenerateConditions->None] Missing Macro Error Failure Skip - symbolical successful subtest Successful [Tested: 3]
6.2.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\int_{x}^{\infty}\frac{e^{-t}}{t}\diff{t} = -\expintE@{x}} - int((exp(- t))/(t), t = x..infinity) = - Ei(x) - Integrate[Divide[Exp[- t],t], {t, x, Infinity}, GenerateConditions->None] == - ExpIntegralE[1, x] Failure Failure
Failed [3 / 3]
3/3]: [[3.201265867 <- {x = 1.5}
-.1055536899 <- {x = .5}
 Successful [Tested: 3]
6.2.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEi@{+ x} = -\expintEin@{- x}+\ln@@{x}+\EulerConstant} Error ExpIntegralEi[+ x] == - ExpIntegralE[1, - x] + Ln[- x] + EulerGamma + Log[x]+ EulerGamma Missing Macro Error Failure -
Failed [3 / 3]
{Plus[Complex[-1.5598964379112301, -3.141592653589793], Times[-1.0, Ln[-1.5]]] <- {Rule[x, 1.5]}
Plus[Complex[-0.46128414924312044, -3.141592653589793], Times[-1.0, Ln[-0.5]]] <- {Rule[x, 0.5]}
6.2.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEi@{- x} = -\expintEin@{+ x}+\ln@@{x}+\EulerConstant} Error ExpIntegralEi[- x] == - ExpIntegralE[1, + x] + Ln[+ x] + EulerGamma + Log[x]+ EulerGamma Missing Macro Error Failure -
Failed [3 / 3]
{Plus[-1.5598964379112301, Times[-1.0, Ln[1.5]]] <- {Rule[x, 1.5]}
Plus[-0.46128414924312044, Times[-1.0, Ln[0.5]]] <- {Rule[x, 0.5]}
6.2.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinint@{z} = \int_{0}^{z}\frac{\sin@@{t}}{t}\diff{t}} Si(z) = int((sin(t))/(t), t = 0..z) SinIntegral[z] == Integrate[Divide[Sin[t],t], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
6.2.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \shiftsinint@{z} = -\int_{z}^{\infty}\frac{\sin@@{t}}{t}\diff{t}} Ssi(z) = - int((sin(t))/(t), t = z..infinity) SinIntegral[z] - Pi/2 == - Integrate[Divide[Sin[t],t], {t, z, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
6.2.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\int_{z}^{\infty}\frac{\sin@@{t}}{t}\diff{t} = \sinint@{z}-\tfrac{1}{2}\pi} - int((sin(t))/(t), t = z..infinity) = Si(z)-(1)/(2)*Pi - Integrate[Divide[Sin[t],t], {t, z, Infinity}, GenerateConditions->None] == SinIntegral[z]-Divide[1,2]*Pi Successful Successful - Successful [Tested: 7]
6.2.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosint(z) = -\int_{z}^{\infty}\frac{\cos@@{t}}{t}\diff{t}} Ci((z) ) = - int((cos(t))/(t), t = z..infinity) CosIntegral[(z) ] == - Integrate[Divide[Cos[t],t], {t, z, Infinity}, GenerateConditions->None] Translation Error Translation Error - -
6.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to\infty}\sinint@{x} = \tfrac{1}{2}\pi} limit(Si(x), x = infinity) = (1)/(2)*Pi Limit[SinIntegral[x], x -> Infinity, GenerateConditions->None] == Divide[1,2]*Pi Successful Successful - Successful [Tested: 1]
6.2#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to\infty}\cosint@{x} = 0} limit(Ci(x), x = infinity) = 0 Limit[CosIntegral[x], x -> Infinity, GenerateConditions->None] == 0 Successful Successful - Successful [Tested: 1]
6.2.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinhint@{z} = \int_{0}^{z}\frac{\sinh@@{t}}{t}\diff{t}} Shi(z) = int((sinh(t))/(t), t = 0..z) SinhIntegral[z] == Integrate[Divide[Sinh[t],t], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
6.2.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coshint@{z} = \EulerConstant+\ln@@{z}+\int_{0}^{z}\frac{\cosh@@{t}-1}{t}\diff{t}} Chi(z) = gamma + ln(z)+ int((cosh(t)- 1)/(t), t = 0..z) CoshIntegral[z] == EulerGamma + Log[z]+ Integrate[Divide[Cosh[t]- 1,t], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
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} Error ExpIntegralE[1, z] == ExpIntegralE[1, z] + Ln[z] + EulerGamma - Log[z]- EulerGamma Missing Macro Error Failure -
Failed [7 / 7]
{Plus[Complex[0.0, 0.5235987755982988], Times[-1.0, Ln[Complex[0.8660254037844387, 0.49999999999999994]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.0, 2.0943951023931953], Times[-1.0, Ln[Complex[-0.4999999999999998, 0.8660254037844387]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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} 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]
21/21]: [[-.1e-8+6.283185310*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, m = 3}
-.6e-8+12.56637063*I <- {z = 1/2*3^(1/2)+1/2*I, m = 2, m = 3}
Failed [7 / 7]
{Complex[0.0, 18.84955592153876] <- {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.0, 18.84955592153876] <- {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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} 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]
{Plus[Complex[0.0, 3.6651914291880923], Times[-1.0, Ln[Complex[-0.8660254037844387, -0.49999999999999994]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.0, 5.235987755982989], Times[-1.0, Ln[Complex[0.4999999999999998, -0.8660254037844387]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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} 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]
{Plus[Complex[0.0, -2.6179938779914944], Times[-1.0, Ln[Complex[-0.8660254037844387, -0.49999999999999994]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.0, -1.0471975511965976], Times[-1.0, Ln[Complex[0.4999999999999998, -0.8660254037844387]]]] <- {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}} Ci(z*exp(+ Pi*I)) = + Pi*I + Ci(z) CosIntegral[z*Exp[+ Pi*I]] == + Pi*I + CosIntegral[z] Failure Failure
Failed [2 / 7]
2/7]: [[0.-6.283185308*I <- {z = 1/2*3^(1/2)+1/2*I}
0.-6.283185308*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [2 / 7]
{Complex[0.0, -6.283185307179586] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.0, -6.283185307179586] <- {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}} Ci(z*exp(- Pi*I)) = - Pi*I + Ci(z) CosIntegral[z*Exp[- Pi*I]] == - Pi*I + CosIntegral[z] Failure Failure
Failed [5 / 7]
5/7]: [[0.+6.283185308*I <- {z = 1/2-1/2*I*3^(1/2)}
0.+6.283185308*I <- {z = -1/2*3^(1/2)-1/2*I}
Failed [5 / 7]
{Complex[0.0, 6.283185307179585] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
Complex[0.0, 6.283185307179586] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], 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}} Chi(z*exp(+ Pi*I)) = + Pi*I + Chi(z) CoshIntegral[z*Exp[+ Pi*I]] == + Pi*I + CoshIntegral[z] Failure Failure
Failed [2 / 7]
2/7]: [[0.-6.283185308*I <- {z = 1/2*3^(1/2)+1/2*I}
0.-6.283185307*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [2 / 7]
{Complex[0.0, -6.283185307179586] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.0, -6.283185307179586] <- {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}} Chi(z*exp(- Pi*I)) = - Pi*I + Chi(z) CoshIntegral[z*Exp[- Pi*I]] == - Pi*I + CoshIntegral[z] Failure Failure
Failed [5 / 7]
5/7]: [[0.+6.283185307*I <- {z = 1/2-1/2*I*3^(1/2)}
0.+6.283185308*I <- {z = -1/2*3^(1/2)-1/2*I}
Failed [5 / 7]
{Complex[0.0, 6.283185307179586] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
Complex[0.0, 6.283185307179586] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
6.5.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{-x+ i0} = -\expintEi@{x}- i\pi} Error ExpIntegralE[1, - x + I*0] == - ExpIntegralEi[x]- I*Pi Missing Macro Error Failure - Successful [Tested: 3]
6.5.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{-x- i0} = -\expintEi@{x}+ i\pi} Error ExpIntegralE[1, - x - I*0] == - ExpIntegralEi[x]+ I*Pi Missing Macro Error Failure -
Failed [3 / 3]
{Complex[0.0, -6.283185307179586] <- {Rule[x, 1.5]}
Complex[0.0, -6.283185307179586] <- {Rule[x, 0.5]}
6.5.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEi@{x} = -\tfrac{1}{2}(\expintE@{-x+i0}+\expintE@{-x-i0})} Error ExpIntegralEi[x] == -Divide[1,2]*(ExpIntegralE[1, - x + I*0]+ ExpIntegralE[1, - x - I*0]) Missing Macro Error Failure -
Failed [3 / 3]
{Complex[0.0, -3.141592653589793] <- {Rule[x, 1.5]}
Complex[0.0, -3.141592653589793] <- {Rule[x, 0.5]}
6.5.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(\expintEi@{x}+\expintE@{x}) = \sinhint@{x}} Error Divide[1,2]*(ExpIntegralEi[x]+ ExpIntegralE[1, x]) == SinhIntegral[x] Missing Macro Error Failure - Successful [Tested: 3]
6.5.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinhint@{x} = -i\sinint@{ix}} Shi(x) = - I*Si(I*x) SinhIntegral[x] == - I*SinIntegral[I*x] Successful Successful - Successful [Tested: 3]
6.5.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(\expintEi@{x}-\expintE@{x}) = \coshint@{x}} Error Divide[1,2]*(ExpIntegralEi[x]- ExpIntegralE[1, x]) == CoshIntegral[x] Missing Macro Error Failure Skip - symbolical successful subtest Successful [Tested: 3]
6.5.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coshint@{x} = \cosint@{ix}-\tfrac{1}{2}\pi i} Chi(x) = Ci(I*x)-(1)/(2)*Pi*I CoshIntegral[x] == CosIntegral[I*x]-Divide[1,2]*Pi*I Failure Failure Successful [Tested: 3] Successful [Tested: 3]
6.5.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinint@{z} = \tfrac{1}{2}i(\expintE@{-iz}-\expintE@{iz})+\tfrac{1}{2}\pi} Si(z) = (1)/(2)*I*(Ei(- I*z)- Ei(I*z))+(1)/(2)*Pi SinIntegral[z] == Divide[1,2]*I*(ExpIntegralE[1, - I*z]- ExpIntegralE[1, I*z])+Divide[1,2]*Pi Failure Failure
Failed [5 / 7]
5/7]: [[-3.141592653+0.*I <- {z = 1/2*3^(1/2)+1/2*I}
-3.141592654-.1e-9*I <- {z = 1/2-1/2*I*3^(1/2)}
Failed [2 / 7]
{Complex[-3.141592653589793, 0.0] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[-3.141592653589793, 0.0] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
6.5.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosint@{z} = -\tfrac{1}{2}(\expintE@{iz}+\expintE@{-iz})} Ci(z) = -(1)/(2)*(Ei(I*z)+ Ei(- I*z)) CosIntegral[z] == -Divide[1,2]*(ExpIntegralE[1, I*z]+ ExpIntegralE[1, - I*z]) Failure Failure
Failed [7 / 7]
7/7]: [[.8944744988+.632221722*I <- {z = 1/2*3^(1/2)+1/2*I}
1.393548628+1.498247032*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [2 / 7]
{Complex[0.0, 3.141592653589793] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
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}} 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}} 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]
7/7]: [[1.393548628+1.498247032*I <- {z = 1/2*3^(1/2)+1/2*I}
.8944744989+3.773814377*I <- {z = -1/2+1/2*I*3^(1/2)}
 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}} 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]
7/7]: [[1.393548628+1.498247031*I <- {z = 1/2*3^(1/2)+1/2*I}
.8944744987+3.773814376*I <- {z = -1/2+1/2*I*3^(1/2)}
 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}} 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]
{Plus[Complex[0.0, -0.5235987755982988], Ln[Complex[0.8660254037844387, 0.49999999999999994]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.0, -2.0943951023931953], Ln[Complex[-0.4999999999999998, 0.8660254037844387]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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)}} 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)}} 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]
6.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{e^{-at}}{t+b}\diff{t} = \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\diff{t}} int((exp(- a*t))/(t + b), t = 0..infinity) = int((exp(I*a*t))/(t + I*b), t = 0..infinity) Integrate[Divide[Exp[- a*t],t + b], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Exp[I*a*t],t + I*b], {t, 0, Infinity}, GenerateConditions->None] Successful Aborted Skip - symbolical successful subtest Successful [Tested: 9]
6.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\diff{t} = e^{ab}\expintE@{ab}} int((exp(I*a*t))/(t + I*b), t = 0..infinity) = exp(a*b)*Ei(a*b) Integrate[Divide[Exp[I*a*t],t + I*b], {t, 0, Infinity}, GenerateConditions->None] == Exp[a*b]*ExpIntegralE[1, a*b] Failure Failure
Failed [9 / 9]
9/9]: [[-56.03273673 <- {a = 1.5, b = 1.5}
-1.835422085 <- {a = 1.5, b = .5}
 Successful [Tested: 9]
6.7.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{x}\int_{0}^{\alpha}\frac{e^{-xt}}{1-t}\diff{t} = \expintEi@{x}-\expintEi@{(1-\alpha)x}} Error Exp[x]*Integrate[Divide[Exp[- x*t],1 - t], {t, 0, \[Alpha]}, GenerateConditions->None] == ExpIntegralEi[x]- ExpIntegralEi[(1 - \[Alpha])* x] Missing Macro Error Failure - Successful [Tested: 3]
6.7.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{e^{it}}{a^{2}+t^{2}}\diff{t} = \frac{i}{2a}\left(e^{a}\expintE@{a-ix}-e^{-a}\expintE@{-a-ix}\right)} int((exp(I*t))/((a)^(2)+ (t)^(2)), t = x..infinity) = (I)/(2*a)*(exp(a)*Ei(a - I*x)- exp(- a)*Ei(- a - I*x)) Integrate[Divide[Exp[I*t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == Divide[I,2*a]*(Exp[a]*ExpIntegralE[1, a - I*x]- Exp[- a]*ExpIntegralE[1, - a - I*x]) Failure Aborted
Failed [9 / 9]
9/9]: [[-5.458727175-3.178550596*I <- {a = 1.5, x = 1.5}
-1.924923680-4.406791455*I <- {a = 1.5, x = .5}
 Skipped - Because timed out
6.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{te^{it}}{a^{2}+t^{2}}\diff{t} = \tfrac{1}{2}\left(e^{a}\expintE@{a-ix}+e^{-a}\expintE@{-a-ix}\right)} int((t*exp(I*t))/((a)^(2)+ (t)^(2)), t = x..infinity) = (1)/(2)*(exp(a)*Ei(a - I*x)+ exp(- a)*Ei(- a - I*x)) Integrate[Divide[t*Exp[I*t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Exp[a]*ExpIntegralE[1, a - I*x]+ Exp[- a]*ExpIntegralE[1, - a - I*x]) Failure Aborted
Failed [9 / 9]
9/9]: [[-5.267453009+8.746914637*I <- {a = 1.5, x = 1.5}
-7.302877906+3.948990541*I <- {a = 1.5, x = .5}
 Successful [Tested: 9]
6.7.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{e^{-t}}{a^{2}+t^{2}}\diff{t} = -\frac{1}{2ai}\left(e^{ia}\expintE@{x+ia}-e^{-ia}\expintE@{x-ia}\right)} int((exp(- t))/((a)^(2)+ (t)^(2)), t = x..infinity) = -(1)/(2*a*I)*(exp(I*a)*Ei(x + I*a)- exp(- I*a)*Ei(x - I*a)) Integrate[Divide[Exp[- t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == -Divide[1,2*a*I]*(Exp[I*a]*ExpIntegralE[1, x + I*a]- Exp[- I*a]*ExpIntegralE[1, x - I*a]) Failure Aborted
Failed [9 / 9]
9/9]: [[1.667239755-0.*I <- {a = 1.5, x = 1.5, x = 3/2}
.7611670238-0.*I <- {a = 1.5, x = .5, x = 3/2}
 Skipped - Because timed out
6.7.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{te^{-t}}{a^{2}+t^{2}}\diff{t} = \tfrac{1}{2}\left(e^{ia}\expintE@{x+ia}+e^{-ia}\expintE@{x-ia}\right)} int((t*exp(- t))/((a)^(2)+ (t)^(2)), t = x..infinity) = (1)/(2)*(exp(I*a)*Ei(x + I*a)+ exp(- I*a)*Ei(x - I*a)) Integrate[Divide[t*Exp[- t],(a)^(2)+ (t)^(2)], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Exp[I*a]*ExpIntegralE[1, x + I*a]+ Exp[- I*a]*ExpIntegralE[1, x - I*a]) Failure Aborted
Failed [9 / 9]
9/9]: [[3.610851888+0.*I <- {a = 1.5, x = 1.5, x = 3/2}
2.934911868+0.*I <- {a = 1.5, x = .5, x = 3/2}
 Skipped - Because timed out
6.7.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{e^{-at}\sin@{bt}}{t}\diff{t} = \imagpart@@{\expintEin@{a+ib}}} Error Integrate[Divide[Exp[- a*t]*Sin[b*t],t], {t, 0, 1}, GenerateConditions->None] == Im[ExpIntegralE[1, a + I*b] + Ln[a + I*b] + EulerGamma] Missing Macro Error Failure -
Failed [1 / 1]
{Plus[Complex[0.7167380515760515, 5.551115123125783*^-17], Times[-1.0, Plus[-0.06866011182139653, Im[Ln[Complex[1.5, 1.5]]]]]] <- {Rule[a, Rational[3, 2]], Rule[b, Rational[3, 2]]}
6.7.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{e^{-at}(1-\cos@{bt})}{t}\diff{t} = \realpart@@{\expintEin@{a+ib}}-\expintEin@{a}} Error Integrate[Divide[Exp[- a*t]*(1 - Cos[b*t]),t], {t, 0, 1}, GenerateConditions->None] == Re[ExpIntegralE[1, a + I*b] + Ln[a + I*b] + EulerGamma]- ExpIntegralE[1, a] + Ln[a] + EulerGamma Missing Macro Error Failure -
Failed [1 / 1]
{Plus[Complex[-0.8490131893081223, 0.0], Times[-1.0, Ln[1.5]], Times[-1.0, Plus[-0.04115544978502889, Re[Ln[Complex[1.5, 1.5]]]]]] <- {Rule[a, Rational[3, 2]], Rule[b, Rational[3, 2]]}
6.7.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \shiftsinint@{z} = -\int_{0}^{\pi/2}e^{-z\cos@@{t}}\cos@{z\sin@@{t}}\diff{t}} Ssi(z) = - int(exp(- z*cos(t))*cos(z*sin(t)), t = 0..Pi/ 2) SinIntegral[z] - Pi/2 == - Integrate[Exp[- z*Cos[t]]*Cos[z*Sin[t]], {t, 0, Pi/ 2}, GenerateConditions->None] Failure Aborted
Failed [2 / 7]
2/7]: [[-3.141592654+.1e-9*I <- {z = -1/2+1/2*I*3^(1/2)}
-3.141592653+0.*I <- {z = -1/2*3^(1/2)-1/2*I}
 Skipped - Because timed out
6.7.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\sin@@{t}}{t+z}\diff{t} = \int_{0}^{\infty}\frac{e^{-zt}}{t^{2}+1}\diff{t}} int((sin(t))/(t + z), t = 0..infinity) = int((exp(- z*t))/((t)^(2)+ 1), t = 0..infinity) Integrate[Divide[Sin[t],t + z], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Exp[- z*t],(t)^(2)+ 1], {t, 0, Infinity}, GenerateConditions->None] Failure Successful Error Successful [Tested: 7]
6.7.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\cos@@{t}}{t+z}\diff{t} = \int_{0}^{\infty}\frac{te^{-zt}}{t^{2}+1}\diff{t}} int((cos(t))/(t + z), t = 0..infinity) = int((t*exp(- z*t))/((t)^(2)+ 1), t = 0..infinity) Integrate[Divide[Cos[t],t + z], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[t*Exp[- z*t],(t)^(2)+ 1], {t, 0, Infinity}, GenerateConditions->None] Failure Successful Error Successful [Tested: 7]
6.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\ln@{1+\frac{2}{x}} < e^{x}\expintE@{x}} (1)/(2)*ln(1 +(2)/(x)) < exp(x)*Ei(x) Divide[1,2]*Log[1 +Divide[2,x]] < Exp[x]*ExpIntegralE[1, x] Failure Failure
Failed [1 / 3]
1/3]: [[.8047189560 < .7488820189 <- {x = .5}
 Successful [Tested: 3]
6.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{x}\expintE@{x} < \ln@{1+\frac{1}{x}}} exp(x)*Ei(x) < ln(1 +(1)/(x)) Exp[x]*ExpIntegralE[1, x] < Log[1 +Divide[1,x]] Failure Failure
Failed [2 / 3]
2/3]: [[14.79533491 < .5108256240 <- {x = 1.5}
36.60711558 < .4054651081 <- {x = 2}
 Successful [Tested: 3]
6.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x}{x+1} < xe^{x}\expintE@{x}} (x)/(x + 1) < x*exp(x)*Ei(x) Divide[x,x + 1] < x*Exp[x]*ExpIntegralE[1, x] Failure Failure Successful [Tested: 3] Successful [Tested: 3]
6.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle xe^{x}\expintE@{x} < \frac{x+1}{x+2}} x*exp(x)*Ei(x) < (x + 1)/(x + 2) x*Exp[x]*ExpIntegralE[1, x] < Divide[x + 1,x + 2] Failure Failure
Failed [2 / 3]
2/3]: [[22.19300237 < .7142857143 <- {x = 1.5}
73.21423116 < .7500000000 <- {x = 2}
 Successful [Tested: 3]
6.8.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x(x+3)}{x^{2}+4x+2} < xe^{x}\expintE@{x}} (x*(x + 3))/((x)^(2)+ 4*x + 2) < x*exp(x)*Ei(x) Divide[x*(x + 3),(x)^(2)+ 4*x + 2] < x*Exp[x]*ExpIntegralE[1, x] Failure Failure
Failed [1 / 3]
1/3]: [[.4117647059 < .3744410095 <- {x = .5}
 Successful [Tested: 3]
6.8.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle xe^{x}\expintE@{x} < \frac{x^{2}+5x+2}{x^{2}+6x+6}} x*exp(x)*Ei(x) < ((x)^(2)+ 5*x + 2)/((x)^(2)+ 6*x + 6) x*Exp[x]*ExpIntegralE[1, x] < Divide[(x)^(2)+ 5*x + 2,(x)^(2)+ 6*x + 6] Failure Failure
Failed [2 / 3]
2/3]: [[22.19300237 < .6811594203 <- {x = 1.5}
73.21423116 < .7272727273 <- {x = 2}
 Successful [Tested: 3]
6.10#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{0} = 1} c[0] = 1 Subscript[c, 0] == 1 Skipped - no semantic math Skipped - no semantic math - -
6.10#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1} = -1} c[1] = - 1 Subscript[c, 1] == - 1 Skipped - no semantic math Skipped - no semantic math - -
6.10#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{2} = \tfrac{1}{2}} c[2] = (1)/(2) Subscript[c, 2] == Divide[1,2] Skipped - no semantic math Skipped - no semantic math - -
6.10#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{3} = -\tfrac{1}{3}} c[3] = -(1)/(3) Subscript[c, 3] == -Divide[1,3] Skipped - no semantic math Skipped - no semantic math - -
6.10#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{4} = \tfrac{1}{6}} c[4] = (1)/(6) Subscript[c, 4] == Divide[1,6] Skipped - no semantic math Skipped - no semantic math - -
6.10.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{k} = -\sum_{j=0}^{k-1}\frac{c_{j}}{k-j}} c[k] = - sum((c[j])/(k - j), j = 0..k - 1) Subscript[c, k] == - Sum[Divide[Subscript[c, j],k - j], {j, 0, k - 1}, GenerateConditions->None] Skipped - no semantic math Skipped - no semantic math - -
6.10.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinint@{z} = z\sum_{n=0}^{\infty}\left(\sphBesselJ{n}@{\tfrac{1}{2}z}\right)^{2}} Error SinIntegral[z] == z*Sum[(SphericalBesselJ[n, Divide[1,2]*z])^(2), {n, 0, Infinity}, GenerateConditions->None] Missing Macro Error Successful - Successful [Tested: 7]
6.10.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEi@{x} = \EulerConstant+\ln@@{\abs{x}}+\sum_{n=0}^{\infty}(-1)^{n}(x-a_{n})\left(\modsphBesseli{1}{n}@{\tfrac{1}{2}x}\right)^{2}} Error ExpIntegralEi[x] == EulerGamma + Log[Abs[x]]+ Sum[(- 1)^(n)*(x - Subscript[a, n])*(Sqrt[Divide[Pi, Divide[1,2]*x]/2] BesselI[(-1)^(1-1)*(n + 1/2), n])^(2), {n, 0, Infinity}, GenerateConditions->None] Missing Macro Error Failure -
Failed [3 / 3]
{Plus[2.318604676120101, Times[-1.0, NSum[Times[2.0943951023931953, Power[-1, n], Power[BesselI[Plus[Rational[1, 2], n], n], 2], Plus[1.5, Times[-1, Plus[1, Times[2, n]], Plus[1, Power[-1, Plus[1, n]], EulerGamma, PolyGamma[0, Plus[1, n]]]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}
Plus[0.570151420521586, Times[-1.0, NSum[Times[6.283185307179586, Power[-1, n], Power[BesselI[Plus[Rational[1, 2], n], n], 2], Plus[0.5, Times[-1, Plus[1, Times[2, n]], Plus[1, Power[-1, Plus[1, n]], EulerGamma, PolyGamma[0, Plus[1, n]]]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}
6.10.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintEin@{z} = ze^{-z/2}\left(\modsphBesseli{1}{0}@{\tfrac{1}{2}z}+\sum_{n=1}^{\infty}\dfrac{2n+1}{n(n+1)}\modsphBesseli{1}{n}@{\tfrac{1}{2}z}\right)} Error ExpIntegralE[1, z] + Ln[z] + EulerGamma == z*Exp[- z/ 2]*(Sqrt[Divide[Pi, Divide[1,2]*z]/2] BesselI[(-1)^(1-1)*(0 + 1/2), 0]+ Sum[Divide[2*n + 1,n*(n + 1)]*Sqrt[Divide[Pi, Divide[1,2]*z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], {n, 1, Infinity}, GenerateConditions->None]) Missing Macro Error Failure -
Failed [7 / 7]
{Plus[Complex[0.7449988338501623, -0.19274910655694033], Ln[Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-0.6244291912543926, -0.17523758490546462], NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[n, -1], Power[Plus[1, n], -1], Plus[1, Times[2, n]], Power[Pi, Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[-0.31531322950964413, -1.02230061506208], Ln[Complex[-0.4999999999999998, 0.8660254037844387]], Times[Complex[0.11615580955286336, -1.278760766761026], NSum[Times[Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[n, -1], Power[Plus[1, n], -1], Plus[1, Times[2, n]], Power[Pi, Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Ra
6.11.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = \incGamma@{0}{z}} Ei(z) = GAMMA(0, z) ExpIntegralE[1, z] == Gamma[0, z] Failure Failure
Failed [7 / 7]
7/7]: [[1.393548628+1.498247032*I <- {z = 1/2*3^(1/2)+1/2*I}
.8944744989+3.773814377*I <- {z = -1/2+1/2*I*3^(1/2)}
 Successful [Tested: 7]
6.11.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expintE@{z} = e^{-z}\KummerconfhyperU@{1}{1}{z}} Ei(z) = exp(- z)*KummerU(1, 1, z) ExpIntegralE[1, z] == Exp[- z]*HypergeometricU[1, 1, z] Failure Failure
Failed [7 / 7]
7/7]: [[1.393548628+1.498247032*I <- {z = 1/2*3^(1/2)+1/2*I}
.8944744991+3.773814377*I <- {z = -1/2+1/2*I*3^(1/2)}
 Successful [Tested: 7]
6.13.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{0} = 0.37250\;74107\;81366\;63446\;19918\;66580\dots} x[0] = 0.372507410781366634461991866580 Subscript[x, 0] == 0.372507410781366634461991866580 Skipped - no semantic math Skipped - no semantic math - -
6.14.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\expintE@{t}\diff{t} = \frac{1}{a}\ln@{1+a}} int(exp(- a*t)*Ei(t), t = 0..infinity) = (1)/(a)*ln(1 + a) Integrate[Exp[- a*t]*ExpIntegralE[1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a]*Log[1 + a] Failure Successful
Failed [4 / 4]
4/4]: [[-.1487623676-2.094395103*I <- {a = 1.5}
-.5753641448 <- {a = -.5}
 Successful [Tested: 4]
6.14.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\cosint@{t}\diff{t} = -\frac{1}{2a}\ln@{1+a^{2}}} int(exp(- a*t)*Ci(t), t = 0..infinity) = -(1)/(2*a)*ln(1 + (a)^(2)) Integrate[Exp[- a*t]*CosIntegral[t], {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,2*a]*Log[1 + (a)^(2)] Failure Successful Successful [Tested: 3] Successful [Tested: 3]
6.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\shiftsinint@{t}\diff{t} = -\frac{1}{a}\atan@@{a}} int(exp(- a*t)*Ssi(t), t = 0..infinity) = -(1)/(a)*arctan(a) Integrate[Exp[- a*t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,a]*ArcTan[a] Successful Failure -
Failed [3 / 3]
{-902994.0050351195 <- {Rule[a, 1.5]}
-902991.9106400171 <- {Rule[a, 0.5]}
6.14.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\expintE^{2}@{t}\diff{t} = 2\ln@@{2}} int((Ei(t))^(2), t = 0..infinity) = 2*ln(2) Integrate[(ExpIntegralE[1, t])^(2), {t, 0, Infinity}, GenerateConditions->None] == 2*Log[2] Failure Successful Error Successful [Tested: 1]
6.14.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@@{t}\cosint@{t}\diff{t} = \int_{0}^{\infty}\sin@@{t}\shiftsinint@{t}\diff{t}} int(cos(t)*Ci(t), t = 0..infinity) = int(sin(t)*Ssi(t), t = 0..infinity) Integrate[Cos[t]*CosIntegral[t], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Sin[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] Failure Failure Error
Failed [1 / 1]
{902989.9925173485 <- {}
6.14.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\sin@@{t}\shiftsinint@{t}\diff{t} = -\tfrac{1}{4}\pi} int(sin(t)*Ssi(t), t = 0..infinity) = -(1)/(4)*Pi Integrate[Sin[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,4]*Pi Successful Failure Skip - symbolical successful subtest
Failed [1 / 1]
{-902989.9925173485 <- {}
6.14.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cosint^{2}@{t}\diff{t} = \int_{0}^{\infty}\shiftsinint^{2}@{t}\diff{t}} int((Ci(t))^(2), t = 0..infinity) = int((Ssi(t))^(2), t = 0..infinity) Integrate[(CosIntegral[t])^(2), {t, 0, Infinity}, GenerateConditions->None] == Integrate[(SinIntegral[t] - Pi/2)^(2), {t, 0, Infinity}, GenerateConditions->None] Failure Successful Successful [Tested: 0] Successful [Tested: 1]
6.14.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\shiftsinint^{2}@{t}\diff{t} = \tfrac{1}{2}\pi} int((Ssi(t))^(2), t = 0..infinity) = (1)/(2)*Pi Integrate[(SinIntegral[t] - Pi/2)^(2), {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi Failure Successful Successful [Tested: 0] Successful [Tested: 1]
6.14.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cosint@{t}\shiftsinint@{t}\diff{t} = \ln@@{2}} int(Ci(t)*Ssi(t), t = 0..infinity) = ln(2) Integrate[CosIntegral[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}, GenerateConditions->None] == Log[2] Failure Failure Successful [Tested: 0]
Failed [1 / 1]
{-902996.3337464853 <- {}
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(Ci(Pi*n), n = 1..infinity) = (1)/(2)*(ln(2)- gamma) Sum[CosIntegral[Pi*n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[2]- EulerGamma) Failure Failure Successful [Tested: 0]
Failed [1 / 1]
{Plus[-0.05796575782920621, NSum[CosIntegral[Times[n, Pi]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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((Ssi(Pi*n))/(n), n = 1..infinity) = (1)/(2)*Pi*(ln(Pi)- 1) Sum[Divide[SinIntegral[Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*(Log[Pi]- 1) Failure Failure Successful [Tested: 0]
Failed [1 / 1]
{Plus[-0.22734117306968246, NSum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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((- 1)^(n)* Ci(2*Pi*n), n = 1..infinity) = 1 - ln(2)-(1)/(2)*gamma Sum[(- 1)^(n)* CosIntegral[2*Pi*n], {n, 1, Infinity}, GenerateConditions->None] == 1 - Log[2]-Divide[1,2]*EulerGamma Failure Failure Successful [Tested: 0]
Failed [1 / 1]
{Plus[-0.018244986989288337, NSum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
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((- 1)^(n)*(Ssi(2*Pi*n))/(n), n = 1..infinity) = Pi*((3)/(2)*ln(2)- 1) Sum[(- 1)^(n)*Divide[SinIntegral[2*Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Pi*(Divide[3,2]*Log[2]- 1) Failure Failure Successful [Tested: 0]
Failed [1 / 1]
{Plus[-0.12478648186560967, NSum[Times[Power[-1, n], Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[2, n, Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
6.18#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n} = \int_{0}^{\infty}\frac{te^{-zt}}{1+t^{2}}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}} A[n] = int((t*exp(- z*t))/(1 + (t)^(2))*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity) Subscript[A, n] == Integrate[Divide[t*Exp[- z*t],1 + (t)^(2)]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}, GenerateConditions->None] Failure Aborted
Failed [210 / 210]
210/210]: [[.7485296696+.6226310704*I <- {z = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, n = 1}
.8043767351+.5871300239*I <- {z = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [210 / 210]
{Complex[0.7485296693535908, 0.622631070403298] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.8043767348683764, 0.5871300238783713] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
6.18#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{n} = \int_{0}^{\infty}\frac{e^{-zt}}{1+t^{2}}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}} B[n] = int((exp(- z*t))/(1 + (t)^(2))*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity) Subscript[B, n] == Integrate[Divide[Exp[- z*t],1 + (t)^(2)]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}, GenerateConditions->None] Failure Aborted
Failed [210 / 210]
210/210]: [[.7390515864+.5822189558*I <- {z = 1/2*3^(1/2)+1/2*I, B[n] = 1/2*3^(1/2)+1/2*I, n = 1}
.8115624973+.5498007781*I <- {z = 1/2*3^(1/2)+1/2*I, B[n] = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [210 / 210]
{Complex[0.7390515861602941, 0.5822189558055343] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.8115624970800986, 0.549800778092373] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
6.18#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n} = \int_{0}^{\infty}e^{-zt}\left(\frac{t^{2}}{1+t^{2}}\right)^{n}\diff{t}} C[n] = int(exp(- z*t)*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity) Subscript[C, n] == Integrate[Exp[- z*t]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}, GenerateConditions->None] Failure Aborted
Failed [210 / 210]
210/210]: [[.6165937696+.8168923194*I <- {z = 1/2*3^(1/2)+1/2*I, C[n] = 1/2*3^(1/2)+1/2*I, n = 1}
.7435675872+.7346733636*I <- {z = 1/2*3^(1/2)+1/2*I, C[n] = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [210 / 210]
{Complex[0.6165937693596737, 0.8168923194411848] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.7435675869838186, 0.7346733636356504] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
6.18#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n-1} = A_{n}+\frac{z}{2n}C_{n}} A[n - 1] = A[n]+(z)/(2*n)*C[n] Subscript[A, n - 1] == Subscript[A, n]+Divide[z,2*n]*Subscript[C, n] Skipped - no semantic math Skipped - no semantic math - -
6.18#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{n-1} = \frac{2nB_{n}+zA_{n-1}}{2n-1}} B[n - 1] = (2*n*B[n]+ z*A[n - 1])/(2*n - 1) Subscript[B, n - 1] == Divide[2*n*Subscript[B, n]+ z*Subscript[A, n - 1],2*n - 1] Skipped - no semantic math Skipped - no semantic math - -
6.18#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n-1} = C_{n}+B_{n-1}} C[n - 1] = C[n]+ B[n - 1] Subscript[C, n - 1] == Subscript[C, n]+ Subscript[B, n - 1] Skipped - no semantic math Skipped - no semantic math - -
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