Lamé equation, quantum Euler top and elliptic Bernoulli polynomials. (English) Zbl 1178.11026
A new class of Bernoulli polynomials which are called elliptic generalization of odd Bernoulli polynomials are introduced. This class of polynomials are related to the quantum top and to the classical Lamé operator. Effective ways to compute these new polynomials and their properties are given as well and these are used for the calculation of the coefficients of the Lamé spectral polynomials.
Reviewer: Mehmet Cenkci (Antalya)
MSC:
11B83 | Special sequences and polynomials |
33E10 | Lamé, Mathieu, and spheroidal wave functions |
81R12 | Groups and algebras in quantum theory and relations with integrable systems |