| Title:
|
5-dissections and sign patterns of Ramanujan's parameter and its companion (English) |
| Author:
|
Chern, Shane |
| Author:
|
Tang, Dazhao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1115-1128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
5-dissection |
| Keyword:
|
sign pattern |
| Keyword:
|
Ramanujan's parameter |
| MSC:
|
11F27 |
| MSC:
|
30B10 |
| idZBL:
|
Zbl 07442477 |
| idMR:
|
MR4339114 |
| DOI:
|
10.21136/CMJ.2021.0218-20 |
| . |
| Date available:
|
2021-11-08T16:02:35Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149241 |
| . |
| Reference:
|
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| . |
