In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction R(q) and its reciprocal. We obtain the 5-dissections for functions R(q)R(q²)² and R(q)²/R(q²), which are essentially Ramanujan’s parameter and its companion. Additionally, 5-dissections of the reciprocals of these two functions are derived. These 5-dissection formulas imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.

中文翻译：

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Ramanujan参数及其伴随物的5剖分和符号模式

1998年，Michael Hirschhorn发现了Rogers-Ramanujan连续分数R（q）的5分解式及其倒数。我们获得函数R（q）R（q ²）²和R（q）² / R（q ²）的5个剖析，它们实质上是Ramanujan的参数及其伴侣。此外，还得出了这两个函数的倒数的5个剖视图。这些5剖分公式表示，其级数展开中的系数具有周期符号模式，几乎没有例外。