The convergence behavior of q-continued fractions on the unit circle

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• 作者：Douglas Bowman and James Mc Laughlin
• 关键词：Continued fractions ; Rogers ; Ramanujan
• 刊名：The Ramanujan Journal
• 出版年：2006
• 出版时间：October, 2006
• 年：2006
• 卷：12
• 期：2
• 页码：185-195
• 全文大小：272 KB

文摘

In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a wider class of q-continued fractions, a class which includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fractions. We show, for each q-continued fraction, G(q), in this class, that there is an uncountable set of points, Y _G , on the unit circle such that if y ∊ Y _G then G(y) does not converge to a finite value.