  In this paper we determine the asymptotics of the determinant of Bessel
operators for sufficiently smooth generating functions. These operators are
similar to Wiener-Hopf operators with the Fourier transform replaced by the
Hankel transform and thus the asymptotics of the determinanst are similar to
the well-known Szeg\"o-Akhiezer-Kac formula for truncated Wiener-Hopf
determinants. In order to compute the above, we also show that the Bessel
operators differ from the Wiener-Hopf by a Hilbert-Schmidt operator.
