Orthogonality with respect to a Jacobi differential operator and applications

TL;DR

This paper investigates the algebraic and analytic properties of polynomials orthogonal with respect to a Jacobi differential operator and explores a fluid dynamics model related to flow stagnation points.

Contribution

It introduces new properties of Jacobi-orthogonal polynomials and applies these findings to a fluid dynamics problem involving stagnation points.

Findings

Characterization of orthogonal polynomials with Jacobi differential operator

Application of polynomial properties to fluid flow stagnation points

Development of a mathematical model for source point locations in fluid dynamics

Abstract

In this manuscript we study algebraic and analytic properties of the sequence of monic polynomials orthogonal with respect to a Jacobi differential operator. A fluid dynamics model for source points location of a flow of an incompressible fluid with preassigned stagnation points is also considered.