Identities for sin(x) that came from medical imaging

TL;DR

This paper presents novel nonlinear differential identities for sine functions derived from medical imaging research, linking them to non-commutative binomial formulas and complex analysis, with implications for open mathematical problems.

Contribution

It introduces new differential identities for sine functions originating from medical imaging, connecting them to non-commutative algebra and complex analysis.

Findings

Identities resemble non-commutative binomial formulas

Connections to separate analyticity theorems in complex variables

Discussion of open problems in the field

Abstract

The article describes interesting nonlinear differential identities satisfied by standard exponential and trigonometric functions, which appeared as byproducts of medical imaging research. They look like some kind of non-commutative binomial formulas. A brief description of the origin of these identities is provided, as well as their direct algebraic derivation. Relations with separate analyticity theorems in several complex variables and some open problems are also mentioned.