On regularized numerical inversion of Mellin transform Original Research Article

A method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts Mellin transform to Laplace transform, then a regularization method is used to recover the original function of the Mellin transform. The performance of the method is illustrated by the inversion of the test functions available in the literature [J. Inst. Math. & Appl. 20 (1977) 73; SIAM J. Sci. & Stat. Comput 2 (1983) 164]. Results are shown in the tables and diagrams.