# On the higher derivates of arctan

## TL;DR

This paper derives a rational closed-form expression for the higher derivatives of arctan, linking it to Chebyshev polynomials, trigonometric expansions, and Appell sequences, enhancing understanding of its mathematical properties.

## Contribution

It introduces a new rational closed-form formula for higher derivatives of arctan and explores its connections to classical polynomial sequences.

## Key findings

- Derived a rational closed-form expression for higher derivatives of arctan
- Established links between arctan derivatives and Chebyshev polynomials
- Discussed relations to trigonometric expansions and Appell sequences

## Abstract

WWe give a rational closed form expression for the higher derivatives of the inverse tangent function and discuss its relation to Chebyshev polynomials, trigonometric expansions and Appell sequences of polynomials.