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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 UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  In this thesis we study generalizations of the RogersRamanujan continued fraction. The RogersRamanujan continued fraction arises from a threeterm qdifference equation. We consider (m + 1)term qdifference equations and also a generalization of the continued fraction algorithm called a Gcontinued fraction. We obtain a general expansion of the quotient of two contiguous basic hypergeometric function in arbitrarily many variables as a Gcontinued fraction. A careful interpretation of convergence is given for different cases of this expansion. When a full vector space of solutions of a qdifference 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 Gcontinued fraction in order to obtain convergence. Also, an explicit formula for the approximants of a Gcontinued fraction is given. An application of this formula is used to obtain a combinatorial interpretation of a Gcontinued fraction extension of the RogersRamanujan continued fraction. A combinatorial interpretation of the coefficients of the qdifference equation for a very wellpoised basic hypergeometric series studied by A. Selberg is derived. Finally, the arithmetic properties of a generalization of the RogersRamanujan continued fraction are considered. 
Issue Date:  2001 
Type:  Text 
Language:  English 
Description:  77 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2001. 
URI:  http://hdl.handle.net/2142/86775 
Other Identifier(s):  (MiAaPQ)AAI3017047 
Date Available in IDEALS:  20150928 
Date Deposited:  2001 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois