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Ciolan, Emil-Alexandru and Neiss, Robert Axel (2015). Convergence properties of the classical and generalized Rogers-Ramanujan continued fraction. Res. Number Theory, 1 (1). CHAM: SPRINGER INTERNATIONAL PUBLISHING AG. ISSN 2363-9555

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Abstract

The aim of this paper is to study the convergence and divergence of the Rogers-Ramanujan and the generalized Rogers-Ramanujan continued fractions on the unit circle. We provide an example of an uncountable set of measure zero on which the Rogers-Ramanujan continued fraction R(x) diverges and which enlarges a set previously found by Bowman and Mc Laughlin. We further study the generalized Rogers-Ramanujan continued fractions R-a(x) for roots of unity a and give explicit convergence and divergence conditions. As such, we extend some work of Huang towards a question originally investigated by Ramanujan and some work of Schur on the convergence of R(x) at roots of unity. In the end, we state several conjectures and possible directions for generalizing Schur's result to all Rogers-Ramanujan continued fractions R-a(x).

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ciolan, Emil-Alexandru UNSPECIFIED UNSPECIFIED UNSPECIFIED Neiss, Robert Axel UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-386439
DOI:	10.1007/s40993-015-0016-4
Journal or Publication Title:	Res. Number Theory
Volume:	1
Number:	1
Date:	2015
Publisher:	SPRINGER INTERNATIONAL PUBLISHING AG
Place of Publication:	CHAM
ISSN:	2363-9555
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/38643