Summation of p-Adic Functional Series in Integer Points
Number Theory
2017-05-16 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
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.
Cite
@article{arxiv.1508.05079,
title = {Summation of p-Adic Functional Series in Integer Points},
author = {Branko Dragovich and Andrei Yu. Khrennikov and Natasa Z. Misic},
journal= {arXiv preprint arXiv:1508.05079},
year = {2017}
}
Comments
9 pages, accepted for publication in Filomat. arXiv admin note: text overlap with arXiv:1411.4195