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Mellin transform; expansion of Laguerre polynomials; numerical inversion; discrete least squares approximation; numerical examples
In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function $g(r)$ is represented as an expansion of Laguerre polynomials with respect to the variable $t=ln\ r$. 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 technique is applied to numerical examples.
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