Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486004 |
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Title: | On some polynomials and continued fractions arising in the theory of integrable systems | ||||||
Author: | Grosset, Marie-Pierre J. E. |
ISNI:
0000 0001 3521 2415
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Awarding Body: | Loughborough University | ||||||
Current Institution: | Loughborough University | ||||||
Date of Award: | 2007 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
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.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.486004 | DOI: | Not available | ||||
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