Continued fractions with three limit points

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

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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
Pages (from-to)231-258
Number of pages28
JournalAdvances in Mathematics
Volume192
Issue number2
DOIs
Publication statusPublished - 2005 Apr 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Andrews, G. E., Berndt, B. C., Sohn, J., Yee, A. J., & Zaharescu, A. (2005). Continued fractions with three limit points. Advances in Mathematics, 192(2), 231-258. https://doi.org/10.1016/j.aim.2004.04.004