Exponential, Logarithmic, Sine, and Cosine Integrals - 6.11 Relations to Other Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
6.11.E1	${\displaystyle{\displaystyle E_{1}\left(z\right)=\Gamma\left(0,z\right)}}$ \expintE@{z} = \incGamma@{0}{z}		Ei(z) = GAMMA(0, z)	ExpIntegralE[1, z] == Gamma[0, z]	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]
6.11.E2	${\displaystyle{\displaystyle E_{1}\left(z\right)=e^{-z}U\left(1,1,z\right)}}$ \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] Result: 1.393548628+1.498247032*I Test Values: {z = 1/2*3^(1/2)+1/2*I} Result: .8944744991+3.773814377*I Test Values: {z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Successful [Tested: 7]