Abstract. The Bernoulli Numbers are a sequence of rational numbers applied in various mathematics fields and can be written as a limit with t tending toward zero applied to the nth derivative of the function t/(e^t-1). From this result, the Bernoulli Numbers are written in terms of the Eulerian Numbers. From sucessives derivatives of the function t/(e^t-1) the Euler´s Triangle is obtained and a second triangle which allow to construct a limit to represent Bernoulli Numbers using Eulerian Numbers.

Received: November 10, 2012

AMS Subject Classification: 11B68, 11B34, 11M99

Key Words and Phrases: Bernoulli numbers, Bernoulli polynomials, Eulerian numbers, Euler's triangle

Download paper from here.