Oh, by the way, you're in good company if you're having trouble
getting the branch cuts right.
Today I found the following interesting result in Mathematica:
N[Integrate[1/z, {z, 1, I, -1, -I, 1}]]
0. + 6.28319 I
N[Integrate[Cos[z]/z, {z, 1, I, -1, -I, 1}]]
0. + 6.28319 I
N[Integrate[Sin[z]/z^2, {z, 1, I, -1, -I, 1}]]
0. + 6.28319 I
N[Integrate[Exp[z]/z, {z, 1, I, -1, -I, 1}]]
1.66533*10^-16 + 0. I
Or more simply:
{NIntegrate[Exp[z]/z, {z, 1, I}], N[Integrate[Exp[z]/z, {z, 1, I}]]}
{-1.55771 + 2.51688 I, -1.55771 + 0.946083 I}
This is curious because even the naive computation Ei(I) - Ei(1) gives
the expected thing...
Fredrik
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