6.4

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
6.4.E1	${\displaystyle{\displaystyle E_{1}\left(z\right)=\mathrm{Ein}\left(z\right)-\operatorname{Ln}z-\gamma}}$ \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] 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	${\displaystyle{\displaystyle E_{1}\left(ze^{2m\pi i}\right)=E_{1}\left(z\right)-2m\pi i}}$ \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] 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	${\displaystyle{\displaystyle E_{1}\left(ze^{+\pi i}\right)=\mathrm{Ein}\left(-z\right)-\ln z-\gamma-\pi i}}$ \expintE@{ze^{+\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant-\pi i	${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi}}$	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	${\displaystyle{\displaystyle E_{1}\left(ze^{-\pi i}\right)=\mathrm{Ein}\left(-z\right)-\ln z-\gamma+\pi i}}$ \expintE@{ze^{-\pi i}} = \expintEin@{-z}-\ln@@{z}-\EulerConstant+\pi i	${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi}}$	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	${\displaystyle{\displaystyle\mathrm{Ci}\left(ze^{+\pi i}\right)=+\pi i+\mathrm{Ci}\left(z\right)}}$ \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] 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	${\displaystyle{\displaystyle\mathrm{Ci}\left(ze^{-\pi i}\right)=-\pi i+\mathrm{Ci}\left(z\right)}}$ \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] 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	${\displaystyle{\displaystyle\mathrm{Chi}\left(ze^{+\pi i}\right)=+\pi i+\mathrm{Chi}\left(z\right)}}$ \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] 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	${\displaystyle{\displaystyle\mathrm{Chi}\left(ze^{-\pi i}\right)=-\pi i+\mathrm{Chi}\left(z\right)}}$ \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] 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