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What attempts have been made to prove that $\gamma := \lim_{k\rightarrow \infty} \sum_{k=1}^{n} \frac{1}{k} -\log n$ is transcendental?

Any reference for stuff that has been proved on this constant?

Thanks in advance, Alan.

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closed as no longer relevant by Felipe Voloch, David Loeffler, j.c., quid, Alexandre Eremenko Mar 1 '13 at 21:31

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We do not even now if $\gamma$ is irrational. The Wikipedia page has links to papers showing many formulas involving $\gamma$, and at least one paper (by Sondow) directly suggesting an approach to establish its irrationality. –  Andres Caicedo Mar 1 '13 at 15:46
The question of irrationality is still open. See: en.wikipedia.org/wiki/… –  Eric Naslund Mar 1 '13 at 15:46
Have you tried the reference list on Wikipedia? If yes, please say so in your post (as any other source you might already have searched). If no, maybe you should have before posting… –  Loïc Teyssier Mar 1 '13 at 15:49
Yes I looked at it, I thought someone know something from recent years. You can close this question of mine. Thanks. –  Alan Mar 1 '13 at 16:40