On some polynomials and continued fractions arising in the theory of integrable systems
Marie-Pierre J.E. Grosset
2134/33775
https://repository.lboro.ac.uk/articles/thesis/On_some_polynomials_and_continued_fractions_arising_in_the_theory_of_integrable_systems/9374237
This thesis consists of two parts. In the first part an elliptic generalisation of
the Bernoulli polynomials is introduced and investigated. We first consider the
Faulhaber polynomials which are simply related to the even Bernoulli polynomials
and generalise them in relatwn with the classical Lamé equation using the integrals of
the Korteweg-de-Vries equation. An elliptic version of the odd Bernoulli polynomials is defined in relation to the quantum Euler top. These polynomials are applied to
compute the Lamé spectral polynomials and the densities of states of the Lamé
operators.
In the second part we consider a special class of periodic continued fractions that
we call α-fractions. [Continues.]
2018-07-06 11:35:54
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Mathematical Sciences not elsewhere classified