#### Document Type

Article

#### Publication Date

2008

#### Abstract

We derive closed-form expressions for several new classes of Hurwitzian- and Tasoevian continued fractions, including [0; p − 1, 1, u(a + 2nb) − 1, p − 1, 1, v(a + (2n + 1)b) − 1 ]∞ n=0, [0; c + dmn] ∞n=1 and [0; eun, fvn] ∞n=1. One of the constructions used to produce some of these continued fractions can be iterated to produce both Hurwitzian- and Tasoevian continued fractions of arbitrary long quasi-period, with arbitrarily many free parameters and whose limits can be determined as ratios of certain infinite series. We also derive expressions for arbitrarily long finite continued fractions whose partial quotients lie in arithmetic progressions.

#### Publication Title

Acta Arithmetica

#### ISSN

0065-1036

#### Publisher

Institute of Mathematics, Polish Academy of Sciences

#### Volume

135

#### Issue

3

#### First Page

247

#### Last Page

268

#### Recommended Citation

McLaughlin, J.
(2008).
Some new Families of Tasoevian- and Hurwitzian Continued Fractions.
*Acta Arithmetica, 135*(3), 247-268.
Retrieved from https://digitalcommons.wcupa.edu/math_facpub/52

## Comments

Preprint version is available here.