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In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function $g\left(r\right)$ is represented as an expansion of Laguerre polynomials with respect to the variable $t=lnr$. The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last...