  In this paper we are going to prove two asymptotic formulas for determinants
det(I-K_s), as s goes to infinity, where K_s are the Wiener-Hopf-Hankel
operators acting on L^2[0,s] with the kernels K(x-y)+K(x+y) and K(x-y)-K(x+y),
respectively, and K(t):=sin(t)/(\pi*t). These formulas were conjectured by
Dyson. The identification of the constant term in the asymptotics was an open
problem for a long time.
