Computational and theoretical aspects of iterated generating functions

5.00
Hdl Handle:
http://hdl.handle.net/10545/291078
Title:
Computational and theoretical aspects of iterated generating functions
Authors:
Clapperton, James Anthony
Abstract:
The 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.
Publisher:
University of Derby
Issue Date:
2013
URI:
http://hdl.handle.net/10545/291078
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Faculty of Business, Computing & Law

Full metadata record

DC FieldValue Language
dc.contributor.authorClapperton, James Anthonyen_GB
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.en_GB
dc.language.isoenen
dc.publisherUniversity of Derbyen
dc.subjectIterated generating functionsen_GB
dc.subjectInfinite sequencesen_GB
dc.subjectCatalan polynomialsen_GB
dc.subjectHouseholder's methoden_GB
dc.titleComputational and theoretical aspects of iterated generating functionsen_GB
dc.typeThesis or dissertationen
dc.type.qualificationnamePhDen
dc.type.qualificationlevelDoctoralen
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