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dc.contributor.authorClapperton, James Anthony
dc.date.accessioned2013-05-14T13:36:29Z
dc.date.available2013-05-14T13:36:29Z
dc.date.issued2013
dc.identifier.urihttp://hdl.handle.net/10545/291078
dc.description.abstractThe thesis offers an investigation into the analysis of so-called iterated generating functions and the schemes that produce them. Beginning with the study of some ad hoc scheme formulations, the notion of an iterated generating function is introduced and a mechanism to produce arbitrary finite sequences established. The development of schemes to accommodate infinite sequences leads – in the case of the Catalan sequence – to the discovery of what are termed Catalan polynomials whose properties are examined. Results are formulated for these polynomials through the algebraic adaptation of classical root-finding algorithms, serving as a basis for the synthesis of new generalised results for other infinite sequences and their associated polynomials.
dc.language.isoenen
dc.publisherUniversity of Derbyen
dc.subjectIterated generating functionsen
dc.subjectInfinite sequencesen
dc.subjectCatalan polynomialsen
dc.subjectHouseholder's methoden
dc.titleComputational and theoretical aspects of iterated generating functionsen
dc.typeThesis or dissertationen
dc.type.qualificationnamePhDen
dc.type.qualificationlevelDoctoralen
refterms.dateFOA2019-02-28T13:00:28Z
html.description.abstractThe thesis offers an investigation into the analysis of so-called iterated generating functions and the schemes that produce them. Beginning with the study of some ad hoc scheme formulations, the notion of an iterated generating function is introduced and a mechanism to produce arbitrary finite sequences established. The development of schemes to accommodate infinite sequences leads – in the case of the Catalan sequence – to the discovery of what are termed Catalan polynomials whose properties are examined. Results are formulated for these polynomials through the algebraic adaptation of classical root-finding algorithms, serving as a basis for the synthesis of new generalised results for other infinite sequences and their associated polynomials.


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