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Computational and theoretical aspects of iterated generating functions

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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:571970
Date January 2013
CreatorsClapperton, James Anthony
PublisherUniversity of Derby
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://hdl.handle.net/10545/291078

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