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.
Problems
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Matching problems
The critical mass of the Townes soliton
Find a closed form for the critical mass N_c ≈ 11.7008965246 of the Townes soliton, the collapse threshold of the 2D cubic NLS.
The Madelung constant of rock salt
Find a closed form for the Madelung constant of rock salt, M ≈ 1.7475645946, the alternating lattice sum of unit charges on Z^3.
The Ising-class integral C5
Find a closed form for the Ising-class integral C5 = (4/15)∫ t K0(t)^5 dt ≈ 0.6657598002 of Bailey, Borwein and Crandall.
Feigenbaum's period-doubling constant
Find a closed form for Feigenbaum's period-doubling constant δ ≈ 4.6692016091, known to 10,000 digits but not proven irrational.