Document Type

Article

Publication Date

5-2005

Abstract

In some recent papers, the authors considered regular continued fractions of the form [a0; a, · · · , a | {z } m , a2 , · · · , a2 | {z } m , a3 , · · · , a3 | {z } m , · · · ], where a0 ≥ 0, a ≥ 2 and m ≥ 1 are integers. The limits of such continued fractions, for general a and in the cases m = 1 and m = 2, were given as ratios of certain infinite series. However, these formulae can be derived from known facts about two continued fractions of Ramanujan. Motivated by these observations, we give alternative proofs of the results of the previous authors for the cases m = 1 and m = 2 and also use known results about other q-continued fractions investigated by Ramanujan to derive the limits of other infinite families of regular continued fractions

Publication Title

Mathematical Proceedings of the Cambridge Philosophical Society

ISSN

0305-0041

Publisher

Cambridge University Press

Volume

138

Issue

3

First Page

367

Last Page

381

Comments

Preprint version is available here.

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