To solve globally bounded order $3$ linear differential equations with rational function coefficients, this thesis introduces a
partial $_3F_2$-solver (Section~\ref{3F2 type solution}) and $F_1$-solver (Chapter~\ref{F1 solver}), where $_3F_2$ is the hypergeometric
function $_3F_2(a_1,a_2,a_3;b_1,b_2\,|\,x)$ and $F_1$ is the Appell's $F_1(a,b_1,b_2,c\,|\,x,y).$ To investigate the relations among order
$3$ multivariate hypergeometric functions, this thesis presents two multivariate tools: compute homomorphisms (Algorithm~\ref{hom}) of two
$D$-modules, where $D$ is a multivariate differential ring, and compute projective homomorphisms (Algorithm~\ref{algo ProjHom}) using the
tensor product module and Algorithm~\ref{hom}. As an application, all irreducible order $2$ subsystems from reducible order $3$ systems turn
out to come from Gauss hypergeometric function $_2F_1(a,b;c\,|\,x)$ (Chapter~\ref{chapter applications}). / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the
degree of Doctor of Philosophy. / Fall Semester 2017. / November 16, 2017. / Includes bibliographical references. / Mark van Hoeij, Professor Directing Dissertation; Laura Reina, University Representative; Amod Agashe,
Committee Member; Ettore Aldrovandi, Committee Member; Paolo Aluffi, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_605035 |
| Contributors | Xu, Wen (author), Hoeij, Mark van (professor directing dissertation), Reina, Laura (university representative), Agashe, Amod S. (Amod Sadanand) (committee member), Aldrovandi, Ettore (committee member), Aluffi, Paolo, 1960- (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (79 pages), computer, application/pdf |
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