On Rational Invariant Summation of p-Adic Power Series with Binomial Coefficient
Number Theory
2019-11-19 v3
Abstract
In the work we have considered p-adic functional series with binomial coefficients and discussed its p-adic convergence. Then we have derived a recurrence relation following with a summation formula which is invariant for rational argument. More precisely, we have investigated a sufficient condition under which the p-adic power series converges to a rational invariant sum 0. Finally we have shown application of the invariant summation formula to get some intersting relations involving Bernoulli numbers and Bernoulli polynomials.
Keywords
Cite
@article{arxiv.1910.02842,
title = {On Rational Invariant Summation of p-Adic Power Series with Binomial Coefficient},
author = {Absos Ali Shaikh and Mabud Ali Sarkar},
journal= {arXiv preprint arXiv:1910.02842},
year = {2019}
}
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