Random continued fractions with beta hypergeometric distribution

Gérard Letac; Mauro Piccioni

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arXiv · 1004.1192

Random continued fractions with beta hypergeometric distribution

Gérard Letac·Mauro Piccioni

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Abstract

In a recent paper (Asci \textit{et al.}, 2008) it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function $_{2}F_{1}$. In the present paper we fully exploit a formula due to Thomae (1879) in order to generalize substantially the class of random continuous fractions with a density of the above form. This involves the design of seven particular graphs. Infinite paths on them lead to random continued fractions with an explicit distribution. A careful study about the set of five real parameters leading to a beta-hypergeometric distribution is required, relying on almost forgotten results mainly due to Felix Klein.

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Gérard Letac, Mauro Piccioni. 2010-04-07. Random continued fractions with beta hypergeometric distribution. https://arxiv.org/abs/1004.1192

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