Generalized Integral Transforms via the Series Expressions

Trigonometric Series via Laplace Transforms

Costas J. Efthimiou Department of Physics University of Central Florida Orlando, FL 32816 USA Introduction In another NOTE in this MAGAZINE, the author presented a method [2] that uses the Laplace transform and allows one to find exact values for a large class of convergent series of rational terms. Recently, in this MAGAZINE too, Lesko and Smith [3] revisited the method and demonstrated an ext...

SOME INTEGRAL TRANSFORMS OF THE GENERALIZED k-MITTAG-LEFFLER FUNCTION

In the paper, the authors generalize the notion “k-Mittag-Leffler function”, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function. 1. Preliminaries Throughout this paper, let C, R, R0 , R, Z − 0 , and N denote respectively the sets of com...

Summation of Series via Laplace Transforms

We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Henstock-Kurzweil Integral Transforms

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...