Transcendental Functions with a Complex Twist

TL;DR

This paper explores 3D visualizations of transcendental functions over complex subsets, revealing connections between trigonometric and hyperbolic functions through advanced computer graphics.

Contribution

It introduces novel 3D graphical representations of transcendental functions over complex domains, enhancing understanding of their real-valued subsets and interrelations.

Findings

Visualizations reveal connections between circular and hyperbolic functions.

Enhanced graphical methods improve comprehension of complex transcendental functions.

Supports educational understanding of complex function behavior.

Abstract

In our previous paper, Real Polynomials with a Complex Twist [see http://archives.math.utk.edu/ICTCM/VOL28/A040/paper.pdf], we used advancements in computer graphics that allow us to easily illustrate more complete graphs of polynomial functions that are still accessible to students of many different levels. In this paper we examine the 3D graphical representations of selected transcendental functions over subsets of the complex plane for which the functions are real-valued. We visualize and find connections between circular trigonometric functions and hyperbolic functions.