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.
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Pan et al. (2024) studied this question.
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