Riordan Matrix Representations of Euler's Constant $\gamma$ and Euler's Number $e$

TL;DR

This paper introduces a novel representation of Euler's constant and Euler's number using Riordan matrices, providing a new algebraic perspective on these fundamental constants.

Contribution

It presents the first known Riordan matrix representations for both Euler's constant and Euler's number, expanding the algebraic tools available for their analysis.

Findings

Euler's constant $\gamma$ expressed via Riordan matrices

Euler's number $e$ represented through Riordan matrices

Provides a new algebraic framework for fundamental constants

Abstract

We show that the Euler-Mascheroni constant $\gamma$ and Euler's number $e$ can both be represented as a product of a Riordan matrix and certain row and column vectors.