Continued fractions with three limit points

George E. Andrews, Bruce C. Berndt, Jaebum Sohn, Ae Ja Yee, Alexandru Zaharescu

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

On page 45 in his lost notebook, Ramanujan asserts that a certain q-continued fraction has three limit points. More precisely, if A n /B n denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of A n /B n 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.

Original languageEnglish (US)
Pages (from-to)231-258
Number of pages28
JournalAdvances in Mathematics
Volume192
Issue number2
DOIs
StatePublished - Apr 1 2005

Fingerprint

Limit Point
Ramanujan
Continued fraction
Ramanujan's Lost Notebook
Assertion
Modulo
Quotient
Tend
Denote
Partial
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Andrews, George E. ; Berndt, Bruce C. ; Sohn, Jaebum ; Yee, Ae Ja ; Zaharescu, Alexandru. / Continued fractions with three limit points. In: Advances in Mathematics. 2005 ; Vol. 192, No. 2. pp. 231-258.
@article{a9d995e62de346f39f57d0b2b8499857,
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 A n /B n denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of A n /B n 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.",
author = "Andrews, {George E.} and Berndt, {Bruce C.} and Jaebum Sohn and Yee, {Ae Ja} and Alexandru Zaharescu",
year = "2005",
month = "4",
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",

}

Continued fractions with three limit points. / Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru.

In: Advances in Mathematics, Vol. 192, No. 2, 01.04.2005, p. 231-258.

Research output: Contribution to journalArticle

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

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 A n /B n denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of A n /B n 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 A n /B n denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of A n /B n 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

VL - 192

SP - 231

EP - 258

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -