Continued fractions with three limit points

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• 作者：Andrews ; George E. ; Berndt ; Bruce C. ; Sohn ; Jaebum ; Yee ; Ae Ja ; Zaharescu ; Alexandru
• 关键词：Ramanujan's lost notebook ; Continued fraction ; General convergence of continued fractions ; q-series ; Bauer&ndash ; Muir transformation
• 刊名：Advances in Mathematics
• 出版年：2005
• 出版时间：April 1, 2005
• 年：2005
• 卷：192
• 期：2
• 页码：231-258
• 全文大小：317 K

文摘

On page 45 in his lost notebook, Ramanujan asserts that a certain q-continued fraction has three limit points. More precisely, if A_n/B_n denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of A_n/B_n exists and is explicitly given by Ramanujan. Ramanujan's assertion is proved in this paper. Moreover, general classes of continued fractions with three limit points are established.