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Solutions of Second Order Recurrence Relations

Title: Solutions of Second Order Recurrence Relations.
Name(s): Levy, Giles, author
Van Hoeij, Mark, professor directing dissertation
Van Engelen, Robert A., university representative
Aldrovandi, Ettore, committee member
Aluffi, Paolo, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2010
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: This thesis presents three algorithms each of which returns a transformation from a base equation to the input using transformations that preserve order and homogeneity (referred to as gt-transformations). The first and third algorithm are new and the second algorithm is an improvement over prior algorithms for the second order case. The first algorithm `Find 2F1' finds a gt-transformation to a recurrence relation satisfied by a hypergeometric series u(n) = hypergeom([a+n, b],[c],z), if such a transformation exists. The second algorithm `Find Liouvillian' finds a gt-transformation to a recurrence relation of the form u(n+2) + b(n)u(n) = 0 for some b(n) in C(n), if such a transformation exists. The third algorithm `Database Solver' takes advantage of a large database of sequences, `The On-Line Encyclopedia of Integer Sequences' maintained by Neil A. J. Sloane at AT&T Labs Research. It employs this database by using the recurrence relations that they satisfy as base equations from which to return a gt-transformation, if such a transformation exists.
Identifier: FSU_migr_etd-3099 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Spring Semester, 2010.
Date of Defense: December 4, 2009.
Keywords: Transformations, Difference Equations
Bibliography Note: Includes bibliographical references.
Advisory Committee: Mark van Hoeij, Professor Directing Dissertation; Robert A. van Engelen, University Representative; Ettore Aldrovandi, Committee Member; Paolo Aluffi, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record:
Owner Institution: FSU

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Levy, G. (2010). Solutions of Second Order Recurrence Relations. Retrieved from