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On a Problem of Rubel Concerning the Set of Functions Satisfying All the Algebraic Differential Equations Satisfied by a Given Function
Published online by Cambridge University Press: 20 November 2018
Abstract
For two functions $f$ and
$g$, define
$g\ll f$ to mean that
$g$ satisfies every algebraic differential equation over the constants satisfied by
$f$. The order
$\ll $ was introduced in one of a set of problems on algebraic differential equations given by the late Lee Rubel. Here we characterise the set of
$g$ such that
$g\ll f$, when
$f$ is a given Liouvillian function.
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- Copyright © Canadian Mathematical Society 1998