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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832553525973876736 |
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| author | John Michael Nahay |
| author_facet | John Michael Nahay |
| author_sort | John Michael Nahay |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-22dd8469786d475287e836e43d459956 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-22dd8469786d475287e836e43d4599562025-02-03T05:53:48ZengWileyInternational 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 |
| spellingShingle | John Michael Nahay Powersum formula for differential resolvents International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Powersum formula for differential resolvents |
| title_sort | powersum formula for differential resolvents |
| url | http://dx.doi.org/10.1155/S0161171204210602 |
| work_keys_str_mv | AT johnmichaelnahay powersumformulafordifferentialresolvents |