具有Beta超几何分布的随机连分数
Random continued fractions with beta hypergeometric distribution
摘要：
在最近的一篇论文（Asci \textit{et al.}，2008）中，已经表明某些随机连分数的密度是β密度和超几何函数$_{2}F_{1}$的乘积。本文充分利用了Rumaae（1879）的一个公式，以便将具有上述形式密度的随机连续分式类作实质上的推广。这涉及到七个特殊图形的设计。其上的无限路径导致具有显式分布的随机连分数。一个仔细的研究一组五个真正的参数导致一个β-超几何分布是必要的，依靠几乎被遗忘的结果主要是由于费利克斯克莱因。
英文摘要：
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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