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 Scopus citations

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.

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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