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In a recent paper, Yu. A. Brychkov derived a series of identities for multiples sums of special functions, using generating functions. Among these identities, a particularly interesting one involves multiples sums of Bessel $I_{\nu}$ functions with half-integer indices. We derive here some equivalent identities that involve different kinds of Bessel polynomials, sing a probabilistic approach based on the properties of the Generalized Inverse Gaussian probability density.