A short proof of an identity of Sylvester
We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth's proof and is analogous to Macdonald's proof of a related identity of Milne. The second is Sylvester's own proof of his identity.
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299224313 |
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| _version_ | 1832554320798679040 |
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| author | Gaurav Bhatngar |
| author_facet | Gaurav Bhatngar |
| author_sort | Gaurav Bhatngar |
| collection | DOAJ |
| description | We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth's proof
and is analogous to Macdonald's proof of a related identity of Milne. The second is Sylvester's own proof of his identity. |
| format | Article |
| id | doaj-art-d680b3a340b5417b841833c637610cb4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d680b3a340b5417b841833c637610cb42025-02-03T05:51:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122243143510.1155/S0161171299224313A short proof of an identity of SylvesterGaurav Bhatngar0Department of Mathematics, The Ohio State University, Columbus 43210, OH, USAWe present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth's proof and is analogous to Macdonald's proof of a related identity of Milne. The second is Sylvester's own proof of his identity.http://dx.doi.org/10.1155/S0161171299224313Sylvester's identityLouck's identityMilne's identitycomplete homogeneous symmetric functionmultiple basic hypergeometric series. |
| spellingShingle | Gaurav Bhatngar A short proof of an identity of Sylvester International Journal of Mathematics and Mathematical Sciences Sylvester's identity Louck's identity Milne's identity complete homogeneous symmetric function multiple basic hypergeometric series. |
| title | A short proof of an identity of Sylvester |
| title_full | A short proof of an identity of Sylvester |
| title_fullStr | A short proof of an identity of Sylvester |
| title_full_unstemmed | A short proof of an identity of Sylvester |
| title_short | A short proof of an identity of Sylvester |
| title_sort | short proof of an identity of sylvester |
| topic | Sylvester's identity Louck's identity Milne's identity complete homogeneous symmetric function multiple basic hypergeometric series. |
| url | http://dx.doi.org/10.1155/S0161171299224313 |
| work_keys_str_mv | AT gauravbhatngar ashortproofofanidentityofsylvester AT gauravbhatngar shortproofofanidentityofsylvester |