Applications of Neutrix Calculus to Special Functions in Conjunction with Polygamma Functions

TL;DR

This paper introduces a novel approach to defining polygamma functions for negative integers using neutrix calculus, expanding their applicability and understanding in mathematical analysis.

Contribution

It presents a new method for defining polygamma functions at negative integers through neutrix calculus, which was not previously established.

Findings

Extended the domain of polygamma functions to negative integers

Provided a rigorous mathematical framework using neutrix calculus

Potential applications in special functions and mathematical analysis

Abstract

In this paper we define the polygamma functions $\psi^{(n)}(x)$ for negative integers by using neutrix calculus.