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Title: Computational and theoretical aspects of iterated generating functions
Author: Clapperton, James Anthony
ISNI:       0000 0004 2735 2356
Awarding Body: University of Derby
Current Institution: University of Derby
Date of Award: 2013
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: iterated generating functions ; infinite sequences ; Catalan polynomials ; Householder's method