Lam\'e equation, quantum top and elliptic Bernoulli polynomials

TL;DR

This paper introduces a generalization of odd Bernoulli polynomials connected to the quantum Euler top and applies it to compute spectral polynomial coefficients for the Lamé operator.

Contribution

It presents a novel generalization of Bernoulli polynomials and demonstrates their application to spectral analysis of the Lamé operator.

Findings

New generalized Bernoulli polynomials related to quantum Euler top

Explicit computation of spectral polynomial coefficients for Lamé operator

Enhanced understanding of spectral properties in elliptic differential operators

Abstract

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lam\'e operator.