Abstract
A method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts the Mellin transform to the Laplace transform, then the Laplace transform is converted to the first kind convolution integral equation by a suitable substitution.
The integral equation so obtained is an ill-posed problem and we use the spline regularization to solve it. The performance of the method is illustrated by the inversion of the test functions available in the literature [J. Inst. Math. & Appl. 20 (1977), p. 73], [J. Math. Comp. 53 (1989), p. 589], [J. Sci. Stat. Comp. 4 (1983), p. 164]. The effectiveness of the method is shown by results obtained demonstrated by means of tables and diagrams.
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Iqbal, M. Spline regularization of numerical inversion of Mellin transform. Approx. Theory & its Appl. 16, 1–16 (2000). https://doi.org/10.1007/BF02845223
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DOI: https://doi.org/10.1007/BF02845223