A Generalization of the arctg function

TL;DR

This paper introduces a family of multi-variable continuous functions that extend a classical functional equation of the inverse tangent, broadening the mathematical understanding of arctangent generalizations.

Contribution

It defines a new family of functions and proves they satisfy a generalized functional equation of the inverse tangent.

Findings

The functions are continuous in multiple variables.

They satisfy a generalized arctangent functional equation.

The work extends classical properties of the inverse tangent function.

Abstract

In this paper we define a family of continuous functions of an arbitrary number of variables, and prove that they all satisfy a generalization of one of the classical functional equations of the inverse tangent function.