Authors: Dragović, Branko
Title: On summation of p-adic series
Journal: Contemporary Mathematics
Volume: 704
First page: 127
Last page: 138
Issue Date: 1-Jan-2018
ISSN: 02714132
DOI: 10.1090/conm/704/14164
© 2018 American Mathematical Society. Summation of the p-adic functional series∑ εn n! Pkε(n;x)xn, where Pkε(n; x) is a polynomial in x and n with rational coefficients, and ε = ±1, is considered. The series is convergent in the domain |x|p ≤ 1for all primes p. It is found the general form of polynomials Pkε (n; x) which provide rational sums when x ∈ Z. A class of generating polynomials Aεk(n; x) plays a central role in the summation procedure. These generating polynomials are related to many sequences of integers. This is a brief review with some new results.
Keywords: Generating polynomials | P-adic numbers | P-adic series | Sequences of integers

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