Hypergeometric Solutions of Linear Differential Equations with Rational Function Coefficients
Let L be a second order linear differential equation with rational function coefficients. We want to find a solution (if that exists) of L in terms of 2F1-hypergeometric function. This thesis presents two algorithms to find such solution in the following cases: 1. L has five regular singularities wh...
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| Format: | Others |
| Language: | English English |
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Florida State University
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| Online Access: | http://purl.flvc.org/fsu/fd/FSU_migr_etd-9021 |
| Summary: | Let L be a second order linear differential equation with rational function coefficients. We want to find a solution (if that exists) of L in terms of 2F1-hypergeometric function. This thesis presents two algorithms to find such solution in the following cases: 1. L has five regular singularities where at least one of them is logarithmic. 2. L has hypergeometric solution of degree three, i.e, L is solvable in terms of 2F1(a,b;c | f) where f is a rational function of degree three. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of
Doctor of Philosophy. === Summer Semester, 2014. === June 11, 2014. === Belyi maps, Computer Algebra, Dessin d'enfants, Differential Equations, Hypergeometric functions === Includes bibliographical references. === Mark van Hoeij, Professor Directing Thesis; Robert A. van Engelen, University Representative; Amod Agashe, Committee Member; Ettore Aldrovandi, Committee Member; Eriko Hironaka, Committee Member; Kathleen Petersen, Committee Member. |
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