On a class of biorthogonal polynomials on the unit circle

TL;DR

This paper studies biorthogonal polynomials on the unit circle, providing explicit bounds for asymptotic formulas and exploring electrostatic interpretations of their zeros, advancing understanding of their properties and applications.

Contribution

It explicitly derives bounds for the remainder in Askey's asymptotic formula and offers an electrostatic interpretation for zeros of related para-orthogonal polynomials.

Findings

Explicit bounds for asymptotic remainder terms

Electrostatic interpretation of polynomial zeros

Enhanced understanding of biorthogonal polynomial systems

Abstract

A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by R. Askey for this system. An electrostatic interpretation for the zeros of a class of para-orthogonal polynomials associated with the biorthogonal system is also considered.