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 | URL: | https://api.elsevier.com/content/abstract/scopus_id/85047658904 | Abstract: | © 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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