5-dissections and sign patterns of Ramanujan's parameter and its companion

Chern, Shane ; Tang, Dazhao

Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1115-1128

Abstract (VO)

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 $R(q)R(q^2)^2$ and $R(q)^2/R(q^2)$, 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.

Détail

DOI : 10.21136/CMJ.2021.0218-20

Classification : 11F27, 30B10
Keywords: 5-dissection; sign pattern; Ramanujan's parameter

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