Common eigenfunctions of commuting differential operators of rank 2

TL;DR

This paper investigates common eigenfunctions of certain commuting differential operators of rank 2 with polynomial coefficients, providing specific cases where these eigenfunctions can be explicitly determined.

Contribution

It identifies particular cases of commuting differential operators of rank 2 with polynomial coefficients and finds their common eigenfunctions.

Findings

Explicit common eigenfunctions found in specific cases

Advances understanding of rank 2 commuting differential operators

Provides groundwork for further exploration of polynomial coefficient operators

Abstract

In this paper we find coomon eigenfunctions of commuting differential operators of rank 2 with polynomial coefficients in some partial cases.