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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

Open Access article
 Printed: Jun 1998
  • John Shackell
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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.
MSC Classifications: 34A34, 12H05 show english descriptions Nonlinear equations and systems, general
Differential algebra [See also 13Nxx]
34A34 - Nonlinear equations and systems, general
12H05 - Differential algebra [See also 13Nxx]

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