p-Adic Invariant Summation of Some p-Adic Functional Series

p-Adic Invariant Summation of Some p-Adic Functional Series

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-a...

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Veröffentlicht in:arXiv.org 2014-11
Hauptverfasser: Dragovich, Branko, Misic, Natasa Z
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Sprache:eng
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Combinatorial analysis
Factorials
Infinite series
Mathematics - Mathematical Physics
Mathematics - Number Theory
Number theory
Numbers
Physics - Mathematical Physics
Polynomials
Sequences
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description 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 A_k(n;x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics.
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subjects Combinatorial analysis
Factorials
Infinite series
Mathematics - Mathematical Physics
Mathematics - Number Theory
Number theory
Numbers
Physics - Mathematical Physics
Polynomials
Sequences
title p-Adic Invariant Summation of Some p-Adic Functional Series
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