1 | initial version |

Incomplete Gamma function and the Ei function are indeed related. See the following pages for example.

http://en.wikipedia.org/wiki/Exponential_integral http://en.wikipedia.org/wiki/Incomplete_gamma_function

In this sense, the result of the integration is correct.

There is indeed a subtly of brunch cut. Maxima / Sage defines the brunch cut of the function differently from Mathematica. I tested the Maxima result "-1/x + Ei(x) - gamma(-1, -x)" is indeed continuous on the complex plane. But the same function in Mathematica is not continuous.

2 | No.2 Revision |

Incomplete Gamma function and the Ei function are indeed related. See the following pages for example.

http://en.wikipedia.org/wiki/Exponential_integral http://en.wikipedia.org/wiki/Incomplete_gamma_function

In this sense, the result of the integration is correct.

There is indeed a subtly of brunch cut. Maxima / Sage defines the brunch cut of the function differently from Mathematica. I tested the Maxima result "-1/x + Ei(x) - gamma(-1, -x)" is indeed continuous on the complex ~~plane. ~~plane (i.e. the result has no problem). But the same function in Mathematica is not continuous.

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