#### Document Type

Article

#### Publication Date

2004

#### Abstract

If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued fractions. We apply this theorem to two general classes of q continued fraction to show, that if G(q) is one of these continued fractions and |q| > 1, then either G(q) converges or does not converge in the general sense. We also show that if the odd and even parts of the continued fraction K∞n=1an/1 converge to different values, then limn→∞ |an| = ∞.

#### Publication Title

Journal of Computational and Applied Mathematics

#### ISSN

0377-0427

#### Publisher

Elsevier

#### Volume

172

#### Issue

2

#### First Page

363

#### Last Page

373

#### Recommended Citation

Bowman, D.,
&
McLaughlin, J.
(2004).
A Theorem on Divergence in the General Sense for Continued Fractions.
*Journal of Computational and Applied Mathematics, 172*(2), 363-373.
Retrieved from https://digitalcommons.wcupa.edu/math_facpub/41

## Comments

Preprint version is available here.