Analog of the mean-value theorem for polynomials of special form

TL;DR

This paper introduces a new mean value theorem tailored for specific polynomial forms, focusing on sums at regular polygon vertices, and provides criteria for related equations.

Contribution

It presents a novel mean value theorem for special polynomial forms and analyzes sums over regular polygon vertices, offering new theoretical insights.

Findings

New mean value theorem for special polynomials

Criteria for equations involving sums at polygon vertices

Theoretical framework for polynomial sums on regular polygons

Abstract

In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.