#### 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

#### Recommended Citation

McLaughlin, J.,
&
Wyshinski, N.
(2005).
Ramanujan and the Regular Continued Fraction Expansion of Real Numbers.
*Mathematical Proceedings of the Cambridge Philosophical Society, 138*(3), 367-381.
Retrieved from https://digitalcommons.wcupa.edu/math_facpub/77

## Comments

Preprint version is available here.