Some sufficient conditions of a given series with rational terms converging to an irrational number or a transcdental number

TL;DR

This paper establishes sufficient conditions to identify whether a real number is irrational or transcendental, and demonstrates their application through examples, including those from complex analytic dynamics.

Contribution

It introduces new sufficient conditions for classifying real numbers as irrational or transcendental, with practical applications to complex dynamics examples.

Findings

Conditions successfully distinguish irrational and transcendental numbers

Application to complex analytic dynamics examples

Provides a framework for analyzing series with rational terms

Abstract

In this paper, we propose various sufficient conditions to determine if a given real number is an irrational number or a transcendental number and also apply these conditions to some interesting examples, particularly,one of them comes from complex analytic dynamics