Differential resolvents of minimal order and weight
We will determine the number of powers of α that appear with nonzero coefficient in an α-power linear differential resolvent of smallest possible order of a univariate polynomial P(t) whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent ove...
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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/S016117120440235X |
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| _version_ | 1832565218719301632 |
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| author | John Michael Nahay |
| author_facet | John Michael Nahay |
| author_sort | John Michael Nahay |
| collection | DOAJ |
| description | We will determine the number of powers of α that appear with nonzero coefficient in an α-power linear differential resolvent of smallest possible order of a univariate polynomial P(t) whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of an α-resolvent of smallest possible weight. We will then compute the indicial equation, apparent singularities, and Wronskian of the Cockle α-resolvent of a trinomial and finish with a related determinantal formula. |
| format | Article |
| id | doaj-art-2d250134ad0846408e5bf72986ee8e9a |
| 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-2d250134ad0846408e5bf72986ee8e9a2025-02-03T01:08:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004542867289310.1155/S016117120440235XDifferential resolvents of minimal order and weightJohn Michael Nahay025 Chestnut Hill Lane, Columbus, NJ 08022-1039, USAWe will determine the number of powers of α that appear with nonzero coefficient in an α-power linear differential resolvent of smallest possible order of a univariate polynomial P(t) whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of an α-resolvent of smallest possible weight. We will then compute the indicial equation, apparent singularities, and Wronskian of the Cockle α-resolvent of a trinomial and finish with a related determinantal formula.http://dx.doi.org/10.1155/S016117120440235X |
| spellingShingle | John Michael Nahay Differential resolvents of minimal order and weight International Journal of Mathematics and Mathematical Sciences |
| title | Differential resolvents of minimal order and weight |
| title_full | Differential resolvents of minimal order and weight |
| title_fullStr | Differential resolvents of minimal order and weight |
| title_full_unstemmed | Differential resolvents of minimal order and weight |
| title_short | Differential resolvents of minimal order and weight |
| title_sort | differential resolvents of minimal order and weight |
| url | http://dx.doi.org/10.1155/S016117120440235X |
| work_keys_str_mv | AT johnmichaelnahay differentialresolventsofminimalorderandweight |