Authors: Dragović, Branko
Khrennikov, Andrei Yu
Mišicć, Natasă
Title: Summation of p-adic functional series in integer points
Journal: Filomat
Volume: 31
Issue: 5
First page: 1339
Last page: 1347
Issue Date: 1-Jan-2017
ISSN: 03545180
DOI: 10.2298/FIL1705339D
URL: https://api.elsevier.com/content/abstract/scopus_id/85014624181
Abstract: 
© 2017, University of Nis. All rights reserved. Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The corresponding infinite functional series are divergent in the real case, but they are convergent and have p-adic invariant sums in p-adic cases. We found polynomials which generate all significant ingredients of these series and make connection between their real and p-adic properties. In particular, we found connection of one of our integer sequences with the Bell numbers.
Keywords: Bell numbers | Integer sequences | P-adic invariant summation | P-adic series

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