#### Document Type

Article

#### Publication Date

2006

#### Abstract

In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a wider class of qcontinued fractions, a class which includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fractions. We show, for each q-continued fraction, G(q), in this class, that there is an uncountable set of points, YG, on the unit circle such that if y ∈ YG then G(y) does not converge to a finite value. We discuss the implications of our theorems for the convergence of other q-continued fractions, for example the G¨ollnitz-Gordon continued fraction, on the unit circle.

#### Publication Title

The Ramanujan Journal

#### ISSN

1382-4090

#### Publisher

Springer

#### Volume

12

#### Issue

2

#### First Page

185

#### Last Page

195

#### Recommended Citation

Bowman, D.,
&
McLaughlin, J.
(2006).
The Convergence behavior of q-Continued Fractions on the Unit Circle.
*The Ramanujan Journal, 12*(2), 185-195.
Retrieved from https://digitalcommons.wcupa.edu/math_facpub/64

## Comments

Preprint version is available here.