Geodesic
5-dissections and sign patterns of Ramanujan's parameter and its companion
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1115-1128.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/CMJ.2021.0218-20
Classification : 11F27, 30B10
Keywords: 5-dissection; sign pattern; Ramanujan's parameter 
@article{10_21136_CMJ_2021_0218_20,
     author = {Chern, Shane and Tang, Dazhao},
     title = {5-dissections and sign patterns of {Ramanujan's} parameter and its companion},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1115--1128},
     publisher = {mathdoc},
     volume = {71},
     number = {4},
     year = {2021},
     doi = {10.21136/CMJ.2021.0218-20},
     mrnumber = {4339114},
     zbl = {07442477},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0218-20/}
}
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
SP  - 1115
EP  - 1128
VL  - 71
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0218-20/
DO  - 10.21136/CMJ.2021.0218-20
LA  - en
ID  - 10_21136_CMJ_2021_0218_20
ER  - 
%0 Journal Article
%A Chern, Shane
%A Tang, Dazhao
%T 5-dissections and sign patterns of Ramanujan's parameter and its companion
%J Czechoslovak Mathematical Journal
%D 2021
%P 1115-1128
%V 71
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0218-20/
%R 10.21136/CMJ.2021.0218-20
%G en
%F 10_21136_CMJ_2021_0218_20
Chern, Shane; Tang, Dazhao. 5-dissections and sign patterns of Ramanujan's parameter and its companion. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1115-1128. doi : 10.21136/CMJ.2021.0218-20. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0218-20/

Cité par Sources :