Powersum formula for differential resolvents
We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the...
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Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204210602 |
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doaj-22dd8469786d475287e836e43d4599562020-11-24T23:46:43ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004736537110.1155/S0161171204210602Powersum formula for differential resolventsJohn Michael Nahay025 Chestnut Hill Lane, Columbus, NJ 08022-1039, USAWe will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the α-resolvent. Finally, we use the powersum formula to rediscover Cockle's differential resolvent of a cubic trinomial.http://dx.doi.org/10.1155/S0161171204210602 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
John Michael Nahay |
| spellingShingle |
John Michael Nahay Powersum formula for differential resolvents International Journal of Mathematics and Mathematical Sciences |
| author_facet |
John Michael Nahay |
| author_sort |
John Michael Nahay |
| title |
Powersum formula for differential resolvents |
| title_short |
Powersum formula for differential resolvents |
| title_full |
Powersum formula for differential resolvents |
| title_fullStr |
Powersum formula for differential resolvents |
| title_full_unstemmed |
Powersum formula for differential resolvents |
| title_sort |
powersum formula for differential resolvents |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the α-resolvent. Finally, we use the powersum formula to rediscover Cockle's differential resolvent of a cubic trinomial. |
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http://dx.doi.org/10.1155/S0161171204210602 |
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AT johnmichaelnahay powersumformulafordifferentialresolvents |
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