论文标题
Ramanujan参数及其同伴的5次摩擦和符号模式
5-Dissections and sign patterns of Ramanujan's parameter and its companion
论文作者
论文摘要
1998年，迈克尔·赫希霍恩（Michael Hirschhorn）发现了罗杰斯（Rogers）的5隔离 - 罗杰恩（Ramanujan）继续分数$ r（q）$及其倒数。在本文中，我们获得了功能$ r（q）r（q^2）^2 $和$ r（q）^2/r（q^2）$的5摩尔，这实际上是Ramanujan的参数及其同伴。这两个函数的倒数的5隔离也被得出。这些5次摩擦意味着其系列扩展中的系数具有周期性的符号模式，但很少有例外。
In 1998, Michael Hirschhorn discovered 5-dissections of the Rogers--Ramanujan continued fraction $R(q)$ and its reciprocal. In this paper, we obtain the 5-dissections for functions $R(q)R(q^2)^2$ and $R(q)^2/R(q^2)$, which are essentially Ramanujan's parameter and its companion. 5-Dissections of the reciprocals of these two functions are derived as well. These 5-dissections imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.
