Alternative Orthogonal Rational Functions on a Half Line

TL;DR

This paper introduces a new system of orthogonal rational functions on the half line, establishing their properties and presenting three subsystems with desirable features for mathematical analysis.

Contribution

It defines and analyzes alternative orthogonal rational functions of Jacobi type on [1, ∞), including the development of three subsystems with useful properties.

Findings

Defined new orthogonal rational functions on a half line

Established properties of these functions

Presented three subsystems with advantageous features

Abstract

System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties are presented.