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Let $f:\mathbb{C}\to\mathbb{C}$ given for $f(z)=\int_0^z \frac{1-e^t}{t} dt-\ln z$ and put $g(x,y)=\text{Re}(f(z))$. While using the computer, how to determine the curve $g(x,y)=0$?

Thanks for the help.

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This is just too vague to answer... What do you know about $f$? Why don't you just solve $g(x,y) =0$ for $y$ and plot? What software do you use? – Dirk Nov 21 '11 at 14:32
@Dirk: Ok, i will accept your suggestion. I tried to use maple, but had no success. Thanks – Gardel Nov 21 '11 at 14:45
up vote 3 down vote accepted

Using Mathematica:

ContourPlot[With[{z = x + I y},
                  Re[EulerGamma - ExpIntegralEi[z]]] == 0,
             {x, -20, 20}, {y, -20, 20}]

exponential integral contour

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You said you have Maple. I assume it would have the exponential integral available. Search the docs on how that function is used, as well as how to do contour plots. – J. M. Nov 21 '11 at 17:56
Thank you.. one question: How do I install the Mathematica Program? He is free? – Gardel Nov 21 '11 at 18:01
It's not free. There is a trial version however. – J. M. Nov 21 '11 at 18:04
Another question: and analytically? – Gardel Nov 21 '11 at 18:06
It's sorta kinda complicated... – J. M. Nov 21 '11 at 18:12

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