Comment #6 on issue 1092 by asmeurer: limit(sum(1/k, (k, 1, n))-log(n), n, oo) should do it
http://code.google.com/p/sympy/issues/detail?id=1092

We have EulerGamma implemented already, btw:

In [12]: EulerGamma
Out[12]: EulerGamma

In [13]: EulerGamma.evalf()
Out[13]: 0.577215664901533

And if limit can't do it, it should raise NotImplementedError. See issue 2130.

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