On q-series and continued fractions

On the values of continued fractions: q-series

Using the Poincaré–Perron theorem on the asymptotics of the solutions of linear recurrences it is proved that for a class of q-continued fractions the value of the continued fraction is given by a quotient of the solution and its q-shifted value of the corresponding qfunctional equation. r 2003 Elsevier Inc. All rights reserved.

The q-tangent and q-secant numbers via continued fractions

It is well known that the (−1)-evaluation of the enumerator polynomials of permutations (resp. derangements) by the number of excedances gives rise to tangent numbers (resp. secant numbers). Recently, two distinct q-analogues of the latter result have been discovered by Foata and Han, and Josuat-Vergès, respectively. In this paper, we will prove some general continued fractions expansions formu...

Algebraic continued fractions in F q ( ( T −

Beta-continued Fractions over Laurent Series

The present paper is devoted to a new notion of continued fractions in the field of Laurent series over a finite field. The definition of this kind of continued fraction algorithm is based on a general notion of number systems. We will prove some ergodic properties and compute the Hausdorff dimensions of bounded type continued fraction sets.

Continued Fractions of Tails of Hypergeometric Series

The tails of the Taylor series for many standard functions such as arctan and log can be expressed as continued fractions in a variety of ways. A surprising side effect is that some of these continued fractions provide a dramatic acceleration for the underlying power series. These investigations were motivated by a surprising observation about Gregory’s series. Gregory’s series for π, truncated...