A new proof of some identities of Bressoud
We provide a new proof of the following two identities due to Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(5m+1)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers-Ramanujan identities....
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202110155 |
| id |
doaj-648b915399b4453eb5200084decc08fc |
|---|---|
| record_format |
Article |
| spelling |
doaj-648b915399b4453eb5200084decc08fc2020-11-25T00:50:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01321062763310.1155/S0161171202110155A new proof of some identities of BressoudRobin Chapman0School of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, UKWe provide a new proof of the following two identities due to Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(5m+1)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers-Ramanujan identities.http://dx.doi.org/10.1155/S0161171202110155 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Robin Chapman |
| spellingShingle |
Robin Chapman A new proof of some identities of Bressoud International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Robin Chapman |
| author_sort |
Robin Chapman |
| title |
A new proof of some identities of Bressoud |
| title_short |
A new proof of some identities of Bressoud |
| title_full |
A new proof of some identities of Bressoud |
| title_fullStr |
A new proof of some identities of Bressoud |
| title_full_unstemmed |
A new proof of some identities of Bressoud |
| title_sort |
new proof of some identities of bressoud |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
We provide a new proof of the following two identities due to
Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(5m+1)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers-Ramanujan identities. |
| url |
http://dx.doi.org/10.1155/S0161171202110155 |
| work_keys_str_mv |
AT robinchapman anewproofofsomeidentitiesofbressoud AT robinchapman newproofofsomeidentitiesofbressoud |
| _version_ |
1725247133721821184 |