ON THE EXPANSION OF A CONTINUED FRACTION OF ORDER TWELVE

被引：13
|
作者：
Lin, Bernard L. S. [1 ]
机构：
[1] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 08期
基金：
美国国家科学基金会;
关键词：
Continued fraction; dissection; power series expansion; periodicity of sign of coefficients; INFINITE PRODUCTS; RAMANUJAN; COEFFICIENTS; GORDON;
D O I：
10.1142/S1793042113500723
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study 2-, 3-, 4-, 6- and 12-dissections of a continued fraction of order twelve. Our main result is that when the aforementioned continued fraction and its reciprocal are expanded as power series, the sign of the coefficients is periodic, with period 12.
引用
收藏
页码：2019 / 2031
页数：13
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