The family of Eulerian constants in the isodimensional discrete calculus

TL;DR

This paper explores the role of Eulerian constants within the framework of isodimensional discrete calculus, highlighting differences from standard calculus and interpreting the origin of these constants in the new context.

Contribution

It introduces a novel interpretation of Eulerian constants in isodimensional discrete calculus, expanding understanding of their origin and significance.

Findings

Interpretation of Euler's constant in IDC

Analysis of other constants in the same family

Differences between standard and isodimensional calculus

Abstract

Discrete Euclidian Spaces (DESs) are the starting point in the study of the major fields of the Isodimensional Discrete Mathematics (IDM). The isodimensional analysis is not an exception, being particularly interesting and fruitful the presence of the DESs in the study of differential and integral calculus. At the moment, and because of the novelty, the discrepancies between the standard and the isodimensional discrete calculus (IDC) are what draw more attention. As a small sample, in this paper we will see the interpretation given by the IDC about the origin and nature of the constant of Euler, and after that, we will also do likewise with another pair of constants of the same family.