Bell polynomials and generalized Laplace transforms

TL;DR

This paper introduces a generalized Laplace transform using Laguerre-type exponentials, linking Bell polynomials to transform solutions of the Blissard problem, and develops computational methods for these transforms.

Contribution

It presents a novel extension of the Laplace transform based on Bell polynomials and Laguerre-type exponentials, enabling new analytical and computational techniques.

Findings

Extended Laplace transform using Laguerre-type exponentials

Connected Bell polynomials to the Blissard problem

Derived computational methods for the new transforms

Abstract

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical sequence a Laplace-type transform depending on that sequence. Computational techniques for the corresponding transform of analytic functions, involving Bell polynomials, are derived.