Minimal cubature rules on an unbounded domain

TL;DR

This paper introduces a novel family of minimal cubature rules on unbounded domains, utilizing orthogonal polynomials with common zeros, marking the first such development in this area.

Contribution

It constructs the first known family of minimal cubature rules on unbounded domains using orthogonal polynomials with common zeros.

Findings

Established a new family of minimal cubature rules on unbounded domains

Constructed orthogonal polynomials with common zeros on the domain

Demonstrated the rules' optimality and applicability

Abstract

A family of minimal cubature rules is established on an unbounded domain, which is the first such family known on unbounded domains. The nodes of such cubature rules are common zeros of certain orthogonal polynomials on the unbounded domain, which are also constructed.