Powersum formula for polynomials whose distinct roots are differentially independent over constants
We prove that the author's powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic zero provided the distinct roots of the po...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202202331 |
| id |
doaj-a46cd8d2e52c49c9b691f920b1bdb4b7 |
|---|---|
| record_format |
Article |
| spelling |
doaj-a46cd8d2e52c49c9b691f920b1bdb4b72020-11-24T23:57:32ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01321272173810.1155/S0161171202202331Powersum formula for polynomials whose distinct roots are differentially independent over constantsJohn Michael Nahay025 Chestnut Hill Lane, Columbus, NJ 08022-1039, USAWe prove that the author's powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic zero provided the distinct roots of the polynomial are differentially independent over constants. By definition, the terms of a resolvent lie in the differential field generated by the coefficients of the polynomial, and each of the roots of the polynomial are solutions of the resolvent. One example shows how the powersum formula works. Another example shows how the proof that the formula is not zero works.http://dx.doi.org/10.1155/S0161171202202331 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
John Michael Nahay |
| spellingShingle |
John Michael Nahay Powersum formula for polynomials whose distinct roots are differentially independent over constants International Journal of Mathematics and Mathematical Sciences |
| author_facet |
John Michael Nahay |
| author_sort |
John Michael Nahay |
| title |
Powersum formula for polynomials whose distinct roots are differentially independent
over constants |
| title_short |
Powersum formula for polynomials whose distinct roots are differentially independent
over constants |
| title_full |
Powersum formula for polynomials whose distinct roots are differentially independent
over constants |
| title_fullStr |
Powersum formula for polynomials whose distinct roots are differentially independent
over constants |
| title_full_unstemmed |
Powersum formula for polynomials whose distinct roots are differentially independent
over constants |
| title_sort |
powersum formula for polynomials whose distinct roots are differentially independent
over constants |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
We prove that the author's powersum formula yields a
nonzero expression for a particular linear ordinary differential
equation, called a resolvent, associated with a
univariate polynomial whose coefficients lie in a differential
field of characteristic zero provided the distinct roots of the
polynomial are differentially independent over constants. By
definition, the terms of a resolvent lie in the differential field
generated by the coefficients of the polynomial, and each of the
roots of the polynomial are solutions of the resolvent. One
example shows how the powersum formula works. Another example
shows how the proof that the formula is not zero works. |
| url |
http://dx.doi.org/10.1155/S0161171202202331 |
| work_keys_str_mv |
AT johnmichaelnahay powersumformulaforpolynomialswhosedistinctrootsaredifferentiallyindependentoverconstants |
| _version_ |
1725453392748216320 |