INVERSION OF THE FINITE MELLIN TRANSFORM THROUGH SERIES EXPANSIONS

In this paper, we invert the nite Mellin transform by using two dierent methods. The rst one is based on the expansion of the unknown data following the shifted Legendre polynomials. The second one is based on the use of Bessel's functions of the rst kind and order as well as their positive zeros. As an application of this work, we give an ecient method of the inversion of Laplace transform. Several numerical results are given to illustrate the theoretical results.