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

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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 particularly, we have investigated certain condition so that the p-adic series converges and gives rational sum for rational variable.

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• B Dragovich
B. Dragovich, p-adic invariant summation of some p-adic Functional series, p-adic numbers, ultrametric analysis and applications, 2014.
On summation of p-adic series, communications in contemporary mathematics
• B Dragovich
B. Dragovich, On summation of p-adic series, communications in contemporary mathematics, 2017.
• B Andrew
Andrew, B., An introduction to p-adic numbers and p-adic analysis, URL:https://www.maths.gla.ac.uk/ ∼ajb.