Ramanujan三次连分数与12阶连分数的关系及其计算

Pub Date : 2018-01-01 DOI:10.5666/KMJ.2018.58.2.319

B. R. S. Kumar, H. C. Vidya

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引用次数: 0

摘要

本文建立了n = 1、2、3、5、7时的12阶连分数U(- q)与Ramanujan的三次连分数G(- q)和G(q)之间的关系。我们还利用Ramanujan函数的两个参数及其显式值来计算U(q)和U(- q)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Relations between Ramanujan's cubic continued fraction and a continued fraction of order 12 and its evaluations

In the present paper, we establish relationship between continued fraction U(−q) of order 12 and Ramanujan’s cubic continued fraction G(−q) and G(q) for n = 1, 2, 3, 5 and 7. Also we evaluate U(q) and U(−q) by using two parameters for Ramanujan’s theta-functions and their explicit values.

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