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

Comments

Preprint version is available here.

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