The functions studied in the paper are quaternion-valued of a quaternionic variable. It is shown that left slice regular and right related by particular involution, intrinsic play central role theory functions. relation between functions, revealed. As an application, classical Laplace transform generalized naturally to quaternions two different ways, which function real variable or function. us...

In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponential Riordan arrays are the main vehicles used for this.

We deal with a class of one-parameter family integral transforms Bargmann type arising as dual transform fractional Hankel transform. Their ranges are identified to be special subspaces of...

We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.

*Correspondence: Rudolf A. Treumann, International Space Science Institute, ISSI, Hallerstrasse 6, CH-3012 Bern, Switzerland e-mail: [email protected] A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equat...