# A reformulated series expansion of the arctangent function

## TL;DR

This paper presents a new real rational function representation of a previously complex-number-based series expansion of the arctangent function, simplifying its computation and analysis.

## Contribution

It reformulates a complex series expansion of arctangent into a real rational function, enhancing understanding and potential applications.

## Key findings

- The arctangent series can be expressed as a real rational function.
- Simplification from complex to real form facilitates computational efficiency.
- The new representation may improve numerical methods involving arctangent.

## Abstract

In our recent publication we obtained a series expansion of the arctangent function involving complex numbers. In this work we show that this formula can also be expressed as a real rational function.