Nombres de Bernoulli et une formule de Ramanujan

TL;DR

This paper explores the relationship between the Euler-Maclaurin formula and Rota-Baxter equations, and provides a simple proof of Ramanujan's formula for summing specific exponential series.

Contribution

It establishes a novel connection between classical summation formulas and algebraic structures, and offers an accessible proof of Ramanujan's exponential series summation.

Findings

Link between Euler-Maclaurin and Rota-Baxter equations

Simplified proof of Ramanujan's exponential series formula

Enhanced understanding of summation techniques

Abstract

In the first part we establish a connection between the Euler-Maclaurin summation formula and the Rota-Baxter functional equation. In the second part we give a simple proof of a formula, due to Ramanujan, on the summation of certain exponential series.