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Permanent link (DOI): https://doi.org/10.7939/R36H0W

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New formulae for higher order derivatives and a new algorithm for numerical integration Open Access

Descriptions

Other title
Subject/Keyword
Rational approximants
Tail probabilities
Higher order derivatives
Numerical integration
G transformation
Extrapolation methods
Slevinsky-Safouhi formula
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Slevinsky, Richard
Supervisor and department
Lau, Anthony (Mathematical and Statistical Sciences)
Safouhi, Hassan (Campus Saint-Jean and Adjunct Mathematical and Statistical Sciences)
Examining committee member and department
Lau, Anthony (Mathematical and Statistical Sciences)
Dai, Feng (Mathematical and Statistical Sciences)
Penin, Alexander (Physics)
Safouhi, Hassan (Campus Saint-Jean and Adjunct Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2011-09-14T21:59:26Z
Graduation date
2011-11
Degree
Master of Science
Degree level
Master's
Abstract
This thesis is concerned with the development of new formulae for higher order derivatives, and the algorithmic, numerical, and analytical development of the G transformation, a method for computing infinite-range integrals. We introduce the Slevinsky-Safouhi formulae I and II with applications, we develop an algorithm for the G transformation, we derive explicit approximations to incomplete Bessel functions and tail probabilities of five probability distributions from the recursive algorithm for the G transformation, and we present all extant work on the analysis of the convergence properties of the G transformation.
Language
English
DOI
doi:10.7939/R36H0W
Rights
License granted by Richard Slevinsky (rms8@ualberta.ca) on 2011-09-13T21:39:02Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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