## Joint differential resolvents for pseudopolynomials

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Nahay, John Michael

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##### Abstract

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The existence of linear differential resolvents for z^alpha for any root z of
an ordinary polynomial with coefficients in a given ordinary differential field
has been established, where alpha is an indeterminate constant with respect to
the derivation of the given field. In this paper we consider several alphas. We
will call a finite sum of indeterminate powers of a variable v a
pseudopolynomial in v. We will generalize the definition of a differential
resolvent of a single polynomial for a single monomial z^alpha to the
definition of a differential resolvent of several polynomials for a
pseudopolynomial in the roots. We will also generalize the definition of a
resolvent to have non-consecutive derivatives. We will show that the authors
powersum formula may be used to compute this more general differential
resolvent.

Comment: 24 pages, 0 figures, East Coast Computer Algebra Day 2005 and 2007

Comment: 24 pages, 0 figures, East Coast Computer Algebra Day 2005 and 2007

##### Keywords

Mathematics - Rings and Algebras, Mathematics - Classical Analysis and ODEs, 12H05, 13N15