An Explicit Identity to solve sums of Powers of Complex Functions

TL;DR

This paper introduces an explicit identity for calculating sums of powers of complex functions by transforming the problem into a linear system and applying Cramer's rule, avoiding recursive dependencies.

Contribution

It provides a novel explicit formula for sums of powers of complex functions, eliminating the need for recursive calculations.

Findings

Derives a linear system representation for sums of powers of complex functions.

Uses properties of determinants and Cramer's rule to obtain explicit solutions.

Offers a method that avoids recursive dependencies in summation calculations.

Abstract

A recurrence relations for sums of powers of complex functions can be written as a system of linear equation AX=B. Using properties of determinant and Cramer's rule for solving systems of linear equation, this paper presents an absolutely explicit identity for solving sums of powers of complex functions without one sum depends on the others.