Beta-hypergeometric distributions and random continued fractions

The Last of the Hypergeometric Continued Fractions *

A contiguous relation for complementry pairs of very well poised balanced 10φ9 basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan’s Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there ar...

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...

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.

Singularity of Some Random Continued Fractions

We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of GaltonWatson trees. §

Distributions, continued fractions, and the Ehrenfest Urn model