INVERSION OF THE FINITE MELLIN TRANSFORM THROUGH SERIES EXPANSIONS
TAHAR MOUMNI *
Department of Mathematics, University of Cartage, Faculty of Sciences of Bizerte, Bizerte, Tunisia
*Author to whom correspondence should be addressed.
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.
Keywords: Finite mellin transform, shifted legendre polynomials, bessel functions of the rst kind, laplace transform