Re: Did you hear about Euler-Mascheroni integrals?

David W. Cantrell wrote:
Your guess is correct. The most important part of the integral lies near 0,
and so, for large n, a reasonable approximation of I(n) can be obtained by
replacing \infty by 1 and exp(-z) by 1, giving

(-1)^n * \int_0^1 [ln(z)]^n dz

which is indeed n! .

For a better approximation, use more terms of the Maclaurin expansion of
the exponential.

Thanks a lot! :-)

This helps me in proving my guess. But unfortunately I still don't know
where the name Euler-Mascheroni integrals comes from ...


Joachim
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