Abdelmoumène Zekiri, Farid Bencherif
Published 2016-12-10Version 1
The Bernoulli numbers are fascinating and ubiquitous numbers, they occur in several domains of Mathematics like Number theory (FLT), Group theory, Calculus and even in Physics. Since Bernoulli's work, they are yet studied to understand their deep nature and particularly to find relationships between them. In this paper, we give, firstly, a short response to a problem stated, in 1971, by Carlitz and studied by many authors like Prodinger \cite{PRO}, the second pearl is an answer to a question raised, in 2008, by Tom Apostol .The third pearl is another proof of a relationship already given in 2011, by the authors.
Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles
Sums of Products of Bernoulli numbers of the second kind
$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
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