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arXiv · 1910.02842

On Rational Invariant Summation of p-Adic Power Series with Binomial Coefficient

Absos Ali Shaikh·Mabud Ali Sarkar
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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.

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Absos Ali Shaikh, Mabud Ali Sarkar. 2019-10-03. On Rational Invariant Summation of p-Adic Power Series with Binomial Coefficient. https://arxiv.org/abs/1910.02842

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