Quadrature formulas for the Laplace and Mellin transforms

Quadrature formulas for integrals transforms generated by orthogonal polynomials

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...

A note on the comparison between Laplace and Sumudu transforms

The Laplace and Mellin transforms of powers of the Riemann zeta-function

AMS subject classification: Primary 11M06, Secondary 11F72

The h-Laplace and q-Laplace transforms

Article history: Received 12 May 2009 Available online 6 October 2009 Submitted by B.S. Thomson

Mellin Transforms: Harmonic Sums

My assignment is going to introduce the Mellin transform and its application on harmonic sums [1]. Hjalmar Mellin(1854-1933, [2] for a summary of his works) gave his name to the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. Mellin transform is useful to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete prob...