  In this paper we compute the small $x$ asymptotics of the special function
solutions of Painlev\'e-III equation. We use the representation of solution in
terms of Hankel determinants of Bessel functions, which seems to be new. Hankel
determinants can be rewritten as multiple contour integrals using Andr\`eief
identity. Finally small $x$ asymptotics is obtained using elementary asymptotic
methods.
