Gaussian integration with rescaling of abscissas and weights

TL;DR

This paper presents a novel algorithm for integrating polynomial functions with variable weights by extending Gaussian integration through rescaling of abscissas and weights, offering an alternative to interval splitting.

Contribution

The paper introduces a new method that extends Gaussian integration with rescaling, improving flexibility for weighted polynomial integration.

Findings

Effective extension of Gaussian integration for variable weights

Rescaling approach provides accurate integration without interval splitting

Method offers computational advantages over traditional techniques

Abstract

An algorithm for integration of polynomial functions with variable weight is considered. It provides extension of the Gaussian integration, with appropriate scaling of the abscissas and weights. Method is a good alternative to usually adopted interval splitting.