Carlitz’s Identity for the Bernoulli Numbers and Zeon Algebra
Antônio Francisco Neto
DEPRO, Escola de Minas
Campus Morro do Cruzeiro, UFOP
35400-000 Ouro Preto MG
Brazil
Abstract:
In this work we provide a new short proof of Carlitz's identity for the
Bernoulli numbers. Our approach is based on the ordinary generating
function for the Bernoulli numbers and a Grassmann-Berezin integral
representation of the Bernoulli numbers in the context of the Zeon
algebra, which comprises an associative and commutative algebra with
nilpotent generators.
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(Concerned with sequences
A027641
A027642.)
Received January 29 2015; revised version received April 6 2015.
Published in Journal of Integer Sequences, May 25 2015.
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