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Journal of Integer Sequences, Vol. 21 (2018), Article 18.5.1 |
Generalization of an Identity of Apostol
Abdelmoumène Zekiri and Farid Bencherif
LA3C Laboratory
Faculty of Mathematics
USTHB
Algiers
Algeria
Rachid Boumahdi
LA3C-USTHB
École Nationale Supérieure d'Informatique
Algiers
Algeria
Abstract:
We extend and generalize an identity of Apostol
involving Bernoulli numbers, to every sequence of complex numbers.
Moreover, our result allows us to obtain other relations involving
Appell polynomial sequences and second-order linear recurrence
sequences.
(Concerned with sequences
A000032
A000045
A000110
A000129
A001045
A002203
A014551.)
Received December 4 2017; revised versions received April 1 2018; April 2 2018. Published in Journal of Integer Sequences, May 9 2018.
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