IJPAM: Volume 83, No. 4 (2013)
USING EULERIAN NUMBERS
Luciana Massaro Onusic3
1Federal University of Sao Paulo - UNIFESP
2University Nine of July - UNINOVE
3Federal University of Sao Paulo - UNIFESP
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/(et-1). From this result, the Bernoulli Numbers are written in terms of the Eulerian Numbers. From sucessives derivatives of the function t/(et-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
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DOI: 10.12732/ijpam.v83i4.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395