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

Shane Chern; Dazhao Tang

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 1115-1128
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Chern, Shane, and Tang, Dazhao. "5-dissections and sign patterns of Ramanujan's parameter and its companion." Czechoslovak Mathematical Journal 71.4 (2021): 1115-1128. <http://eudml.org/doc/297676>.

@article{Chern2021,
abstract = {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.},
author = {Chern, Shane, Tang, Dazhao},
journal = {Czechoslovak Mathematical Journal},
keywords = {5-dissection; sign pattern; Ramanujan's parameter},
language = {eng},
number = {4},
pages = {1115-1128},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {5-dissections and sign patterns of Ramanujan's parameter and its companion},
url = {http://eudml.org/doc/297676},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Chern, Shane
AU - Tang, Dazhao
TI - 5-dissections and sign patterns of Ramanujan's parameter and its companion
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1115
EP - 1128
AB - 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.
LA - eng
KW - 5-dissection; sign pattern; Ramanujan's parameter
UR - http://eudml.org/doc/297676
ER -

References

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