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 Title: Generalizations of Certain Results on Continued Fraction Author(s): Choi, Geumlan Doctoral Committee Chair(s): Douglas Bowman Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: In this thesis we study generalizations of the Rogers-Ramanujan continued fraction. The Rogers-Ramanujan continued fraction arises from a three-term q-difference equation. We consider (m + 1)-term q-difference equations and also a generalization of the continued fraction algorithm called a G-continued fraction. We obtain a general expansion of the quotient of two contiguous basic hypergeometric function in arbitrarily many variables as a G-continued fraction. A careful interpretation of convergence is given for different cases of this expansion. When a full vector space of solutions of a q-difference equation is known, we use the theorem of Zahar which extends a theorem of Pincherle. When this is not the case, we apply the theory on infinite system of equations to the G-continued fraction in order to obtain convergence. Also, an explicit formula for the approximants of a G-continued fraction is given. An application of this formula is used to obtain a combinatorial interpretation of a G-continued fraction extension of the Rogers-Ramanujan continued fraction. A combinatorial interpretation of the coefficients of the q-difference equation for a very well-poised basic hypergeometric series studied by A. Selberg is derived. Finally, the arithmetic properties of a generalization of the Rogers-Ramanujan continued fraction are considered. Issue Date: 2001 Type: Text Language: English Description: 77 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. URI: http://hdl.handle.net/2142/86775 Other Identifier(s): (MiAaPQ)AAI3017047 Date Available in IDEALS: 2015-09-28 Date Deposited: 2001
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