$On some polynomials and continued fractions arising in the theory of integrable systems$

On some polynomials and continued fractions arising in the theory of integrable systems

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...

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Main Author:	Grosset, Marie-Pierre J. E.
Published:	Loughborough University 2007
Subjects:	512.9422
Online Access:	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486004

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spelling	ndltd-bl.uk-oai-ethos.bl.uk-4860042018-08-07T03:17:10ZOn some polynomials and continued fractions arising in the theory of integrable systemsGrosset, Marie-Pierre J. E.2007This 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.512.9422Loughborough Universityhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486004https://dspace.lboro.ac.uk/2134/33775Electronic Thesis or Dissertation
collection	NDLTD
sources	NDLTD
topic	512.9422
spellingShingle	512.9422 Grosset, Marie-Pierre J. E. On some polynomials and continued fractions arising in the theory of integrable systems
description	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.
author	Grosset, Marie-Pierre J. E.
author_facet	Grosset, Marie-Pierre J. E.
author_sort	Grosset, Marie-Pierre J. E.
title	On some polynomials and continued fractions arising in the theory of integrable systems
title_short	On some polynomials and continued fractions arising in the theory of integrable systems
title_full	On some polynomials and continued fractions arising in the theory of integrable systems
title_fullStr	On some polynomials and continued fractions arising in the theory of integrable systems
title_full_unstemmed	On some polynomials and continued fractions arising in the theory of integrable systems
title_sort	on some polynomials and continued fractions arising in the theory of integrable systems
publisher	Loughborough University
publishDate	2007
url	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486004
work_keys_str_mv	AT grossetmariepierreje onsomepolynomialsandcontinuedfractionsarisinginthetheoryofintegrablesystems
_version_	1718718798768373760

On some polynomials and continued fractions arising in the theory of integrable systems

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