TY - JOUR

T1 - Continued fractions with three limit points

AU - Andrews, George E.

AU - Berndt, Bruce C.

AU - Sohn, Jaebum

AU - Yee, Ae Ja

AU - Zaharescu, Alexandru

N1 - 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.

PY - 2005/4/1

Y1 - 2005/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=13644279376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=13644279376&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2004.04.004

DO - 10.1016/j.aim.2004.04.004

M3 - Article

AN - SCOPUS:13644279376

SN - 0001-8708

VL - 192

SP - 231

EP - 258

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -