@article{4ffdb498b2cc4d399ff73d13cdd4f104,

title = "Continued fractions with three limit points",

abstract = "On page 45 in his lost notebook, Ramanujan asserts that a certain q-continued fraction has three limit points. More precisely, if An/Bn denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of An/Bn exists and is explicitly given by Ramanujan. Ramanujan's assertion is proved in this paper. Moreover, general classes of continued fractions with three limit points are established.",

keywords = "Bauer-Muir transformation, Continued fraction, General convergence of continued fractions, Ramanujan's lost notebook, q-series",

author = "Andrews, {George E.} and Berndt, {Bruce C.} and Jaebum Sohn and Yee, {Ae Ja} and Alexandru Zaharescu",

note = "Funding Information: ·Corresponding author. Fax: +1-217-333-9576. E-mail addresses: andrews@math.psu.edu (G.E. Andrews), berndt@math.uiuc.edu (B.C. Berndt), jsohn@yonsei.ac.kr (J. Sohn), yee@math.psu.edu (A.J. Yee), zaharesc@math.uiuc.edu (A. Zaharescu). 1Research partially supported by Grant DMS-9206993 from the National Science Foundation. 2Research partially supported by Grant MDA904-00-1-0015 from the National Security Agency. 3Research partially supported by the postdoctoral fellowship program from the Korea Science and Engineering Foundation, and by a grant from the Number Theory Foundation.",

year = "2005",

month = apr,

day = "1",

doi = "10.1016/j.aim.2004.04.004",

language = "English (US)",

volume = "192",

pages = "231--258",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "2",

}