5-Ramanujan参数及其伴随参数的剖析和符号模式
5-Dissections and sign patterns of Ramanujan's parameter and its companion
摘要：
1998年，Michael Hirschhorn发现了Rogers-Ramanujan连分数$R(q)$及其倒数的5-剖分.本文给出了函数$R(q)R(q^2)^2$和$R(q)^2/R(q^2)$的5-剖分，它们本质上是Ramanujan参数及其伴随参数. 5-这两个函数的倒数的解剖推导以及。这些5-剖分意味着在它们的级数展开式中的系数具有周期性的符号模式，很少有例外。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
