Some continued fractions in Ramanujan's lost notebook

Jongsil Lee, Jaebum Sohn

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we first give the value of a periodic continued fraction which was recorded incorrectly by Ramanujan on page 341 of his lost notebook. Next, we describe several pairs of equivalent continued fractions in which one is the odd part of the other. One of the results is for the Rogers-Ramanujan continued fraction which was recently proved by Berndt and Yee. Finally, using the Bauer-Muir transformation we prove the equivalence of two continued fractions. One was recorded on page 44 in Ramanujan's lost notebook, and the other is found in the unorganized pages at the end of Ramanujan's second notebook.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalMonatshefte fur Mathematik
Volume146
Issue number1
DOIs
Publication statusPublished - 2005 Sep

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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