6.2

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
6.2.E1	${\displaystyle{\displaystyle E_{1}\left(z\right)=\int_{z}^{\infty}\frac{e^{-t}}{t}\mathrm{d}t}}$ \expintE@{z} = \int_{z}^{\infty}\frac{e^{-t}}{t}\diff{t}	${\displaystyle{\displaystyle z\neq 0}}$	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] 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]
6.2.E2	${\displaystyle{\displaystyle E_{1}\left(z\right)=e^{-z}\int_{0}^{\infty}\frac{e^{-t}}{t+z}\mathrm{d}t}}$ \expintE@{z} = e^{-z}\int_{0}^{\infty}\frac{e^{-t}}{t+z}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$	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] 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]
6.2.E3	${\displaystyle{\displaystyle\mathrm{Ein}\left(z\right)=\int_{0}^{z}\frac{1-e^{-t}}{t}\mathrm{d}t}}$ \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] 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
6.2.E4	${\displaystyle{\displaystyle E_{1}\left(z\right)=\mathrm{Ein}\left(z\right)-\ln z-\gamma}}$ \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
6.2.E6	${\displaystyle{\displaystyle\mathrm{Ei}\left(-x\right)=-\int_{x}^{\infty}\frac{e^{-t}}{t}\mathrm{d}t}}$ \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	${\displaystyle{\displaystyle-\int_{x}^{\infty}\frac{e^{-t}}{t}\mathrm{d}t=-E_{1}\left(x\right)}}$ -\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] Result: 3.201265867 Test Values: {x = 1.5} Result: -.1055536899 Test Values: {x = .5} ... skip entries to safe data	Successful [Tested: 3]
6.2.E7	${\displaystyle{\displaystyle\mathrm{Ei}\left(+x\right)=-\mathrm{Ein}\left(-x\right)+\ln x+\gamma}}$ \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] Result: Plus[Complex[-1.5598964379112301, -3.141592653589793], Times[-1.0, Ln[-1.5]]] Test Values: {Rule[x, 1.5]} Result: Plus[Complex[-0.46128414924312044, -3.141592653589793], Times[-1.0, Ln[-0.5]]] Test Values: {Rule[x, 0.5]} ... skip entries to safe data
6.2.E7	${\displaystyle{\displaystyle\mathrm{Ei}\left(-x\right)=-\mathrm{Ein}\left(+x\right)+\ln x+\gamma}}$ \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] Result: Plus[-1.5598964379112301, Times[-1.0, Ln[1.5]]] Test Values: {Rule[x, 1.5]} Result: Plus[-0.46128414924312044, Times[-1.0, Ln[0.5]]] Test Values: {Rule[x, 0.5]} ... skip entries to safe data
6.2.E9	${\displaystyle{\displaystyle\mathrm{Si}\left(z\right)=\int_{0}^{z}\frac{\sin t}{t}\mathrm{d}t}}$ \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	${\displaystyle{\displaystyle\mathrm{si}\left(z\right)=-\int_{z}^{\infty}\frac{\sin t}{t}\mathrm{d}t}}$ \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	${\displaystyle{\displaystyle-\int_{z}^{\infty}\frac{\sin t}{t}\mathrm{d}t=\mathrm{Si}\left(z\right)-\tfrac{1}{2}\pi}}$ -\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	${\displaystyle{\displaystyle\mathrm{Ci}(z)=-\int_{z}^{\infty}\frac{\cos t}{t}\mathrm{d}t}}$ \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	${\displaystyle{\displaystyle\lim_{x\to\infty}\mathrm{Si}\left(x\right)=\tfrac{1}{2}\pi}}$ \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	${\displaystyle{\displaystyle\lim_{x\to\infty}\mathrm{Ci}\left(x\right)=0}}$ \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	${\displaystyle{\displaystyle\mathrm{Shi}\left(z\right)=\int_{0}^{z}\frac{\sinh t}{t}\mathrm{d}t}}$ \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	${\displaystyle{\displaystyle\mathrm{Chi}\left(z\right)=\gamma+\ln z+\int_{0}^{z}\frac{\cosh t-1}{t}\mathrm{d}t}}$ \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]