Authors: Dragovich, B.
Misic, N. Z.
Title: p-Adic invariant summation of some p-adic functional series
Journal: P-Adic Numbers, Ultrametric Analysis, and Applications
Volume: 6
Issue: 4
First page: 275
Last page: 283
Issue Date: 1-Oct-2014
ISSN: 20700466
DOI: 10.1134/S2070046614040025
URL: https://api.elsevier.com/content/abstract/scopus_id/84946187660
Abstract: 
© 2014, Pleiades Publishing, Ltd. We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients which contain factorials. By recurrence relations, we constructed sequence of polynomials Ak(n; x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics.
Keywords: adelic summation | Bell numbers | Bernoulli numbers | irrational numbers | p-adic numbers | p-adic series | recurrence relations

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