Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus.

May 22, 2019 · Abstract:Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference ...

A novel point of view is presented, embedding dual numbers within a formalism reminiscent of operational umbral calculus, based upon the relevant algebraic ...

Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus.

The main contribution of this paper consists in fixing the underlying algebraic rules of the dual numbers in the wider context of umbral and operational ...

May 2, 2019 · Dual Numbers and their higher order version turned out to be an important tool for 1 numerical computations, and in particular for finite ...

Sep 1, 2024 · Abstract. In this paper, we explore the effectiveness of almost purely operational methods in the study of umbral calculus.

By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage ...

Nov 29, 2023 · This article presents an overview of Umbral calculus and of its wide range of applicability. The aim is to provide new tools, ...

The operational q-additions makes the formulas remarkably pretty. It is well known that there are at least two types of q-Bernoulli numbers, now let us.