Type of Document	Dissertation
Author	Levy, Giles
Author's Email Address	glevy@math.fsu.edu
URN	etd-01042010-235740
Title	Solutions of Second Order Recurrence Relations
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Mark van Hoeij Committee Chair Ettore Aldrovandi Committee Member Paolo Aluffi Committee Member Robert van Engelen University Representative
Keywords	Transformations Difference Equations
Date of Defense	2009-12-04
Availability	unrestricted
Abstract 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.
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