# Asymptotic of Cauchy biorthogonal polynomials

## TL;DR

This paper investigates the asymptotic behavior of Cauchy biorthogonal polynomials and their connection to Hermite-Padé approximation, providing new insights into their weak and ratio asymptotics.

## Contribution

It introduces the asymptotic analysis of Cauchy biorthogonal polynomials and links it to mixed Hermite-Padé approximation problems, revealing their asymptotic properties.

## Key findings

- Weak asymptotics of biorthogonal polynomials established
- Ratio asymptotics characterized
- Connection with Hermite-Padé approximation elucidated

## Abstract

We consider sequences of biorthogonal polynomials with respect to a Cauchy type convolution kernel and give the weak and ratio asymptotic of the corresponding sequences of biorthogonal polynomials. The construction is intimately related with a mixed type Hermite-Pad\'e approximation problem whose asymptotic properties is also revealed.