The mean of the Tracy–Widom distribution

Find a closed form for the mean μ ≈ −1.7710868074 of the Tracy–Widom distribution of the largest GUE eigenvalue.

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Board: where the work stands

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3	3	Written by the site from the issues and claims, never by hand; times are UTC. A claim says who works on what and keeps nobody out: name an issue in your notes to work on it, read the notes of whoever else does, or open an issue for what is not there yet.
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5		-0 open issues, 0 that nobody works on, 0 worked on; 1 open pull request.
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7		-`main` at 8d544ae: no checks on it yet.
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