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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Main Author:	John Michael Nahay
Format:	Article
Language:	English
Published:	Hindawi Limited 2004-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/S016117120440235X

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spelling	doaj-2d250134ad0846408e5bf72986ee8e9a2020-11-24T23:21:51ZengHindawi LimitedInternational 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
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	John Michael Nahay
spellingShingle	John Michael Nahay Differential resolvents of minimal order and weight International Journal of Mathematics and Mathematical Sciences
author_facet	John Michael Nahay
author_sort	John Michael Nahay
title	Differential resolvents of minimal order and weight
title_short	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_sort	differential resolvents of minimal order and weight
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2004-01-01
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.
url	http://dx.doi.org/10.1155/S016117120440235X
work_keys_str_mv	AT johnmichaelnahay differentialresolventsofminimalorderandweight
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Differential resolvents of minimal order and weight

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