基于Lewis和Liu定理的Ramanujan-Selberg连分数及其倒数的2-剖分

2-Dissection of Ramanujan-Selberg Continued Fraction and Its Reciprocal Based on Lewis and Liu Theorem

为了得出Ramanujan-Selberg连分数及其倒数的不同剖分形式,在文中,我们将继续研究Ramanujan-Selberg连分数及其倒数的剖分。首先引入了一些关于连分数的相关定义以及一些定理,然后利用Lewis和Liu的恒等式等相关定理,选取了相关参数得出了Ramanujan-Selberg连分数的2-剖分,根据2-剖分的证明方法,采用不同的参数得到了Ramanujan-Selberg连分数倒数的2-剖分。

In order to obtain the different dissection forms of the Ramanujan-Selberg continued fraction and its reciprocal,this paper will continue to research the dissection of the Ramanujan-Selberg continued fraction and its reciprocal.Firstly,it introduces some relevant definitions and theorems about continued fraction,and then uses the identities of Lewis and Liu.The 2-dissection of the Ramanujan-Selberg continued fraction is obtained by selecting relevant parameters.According to the proof method of 2-dissection,the 2-dissection of the reciprocal of the Ramanujan-Selberg continued fraction is obtained by using different parameters.