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

作　　者：李紫微 LI Ziwei(School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《东莞理工学院学报》2022年第5期13-18,共6页Journal of Dongguan University of Technology

基　　金：重庆市自然科学基金项目(cstc2019jcyjmsxmx0143)。

摘　　要：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.

关 键 词：Ramanujan-Selberg连分数 Lewis-liu恒等式 2-剖分 q-无穷移位阶乘 

分 类 号：O143[理学—数学]