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A closed-form expression is obtained for the conditional probability distribution of t 0 R 2 s ds given Rt, where (Rs, s ≥ 0) is a Bessel process of dimension δ > 0 started from 0, in terms of parabolic cylinder functions. This is done by inverting the following Laplace transform also known as the generalized Lévy's stochastic area formula:doi:10.1556/sscmath.41.2004.1.5 fatcat:h6sqeovfy5cdnop5652brzv6ay