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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
Degree Granting Institution:University of Illinois at Urbana-Champaign
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
Description:77 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
Other Identifier(s):(MiAaPQ)AAI3017047
Date Available in IDEALS:2015-09-28
Date Deposited:2001

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