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

Joint differential resolvents for pseudopolynomials