Fractal algebraic and linguistic structures generated by the Laurent series for the Gamma function near its negative poles

TL;DR

This paper derives explicit Laurent series coefficients for the Gamma function near negative poles, revealing their self-similar, fractal algebraic and linguistic structures.

Contribution

It provides closed-form, self-similar expressions for Laurent coefficients of the Gamma function at negative singularities, highlighting fractal patterns.

Findings

Coefficients have closed-form expressions

Coefficients exhibit self-similar, fractal structures

Algebraic and grammatical patterns identified

Abstract

We give closed-form expressions for the Laurent series coefficients of the Gamma function near all its strictly negative singularities. These closed-form expressions are clearly self-similar. We briefly describe their algebraic and grammatical budding patterns. As the degree of the coefficient grows to infinity its global structure becomes a fractal.