Continued fractions with three limit points

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

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7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)231-258
Number of pages28
JournalAdvances in Mathematics
Issue number2
Publication statusPublished - 2005 Apr 1

Bibliographical note

Funding Information:
·Corresponding author. Fax: +1-217-333-9576. E-mail addresses: (G.E. Andrews), (B.C. Berndt), (J. Sohn), (A.J. Yee), (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.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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