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....
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202110155 |
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| _version_ | 1832563913245327360 |
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| author | Robin Chapman |
| author_facet | Robin Chapman |
| author_sort | Robin Chapman |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-648b915399b4453eb5200084decc08fc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-648b915399b4453eb5200084decc08fc2025-02-03T01:12:19ZengWileyInternational 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 |
| spellingShingle | Robin Chapman A new proof of some identities of Bressoud International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | A new proof of some identities of Bressoud |
| title_sort | new proof of some identities of bressoud |
| url | http://dx.doi.org/10.1155/S0161171202110155 |
| work_keys_str_mv | AT robinchapman anewproofofsomeidentitiesofbressoud AT robinchapman newproofofsomeidentitiesofbressoud |