The five-dimensional Watson integral
Find a closed form for the five-dimensional Watson integral W5 ≈ 0.2312616250, which fixes the return probability of a random walk on Z^5.
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Find a closed form for the five-dimensional Watson integral W5 ≈ 0.2312616250, which fixes the return probability of a random walk on Z^5.
Find a closed form for the mean μ ≈ −1.7710868074 of the Tracy–Widom distribution of the largest GUE eigenvalue.
Find a closed form for the site percolation threshold of the square lattice, p_c ≈ 0.5927460508; bond percolation has p_c = 1/2.