On a problem of Rubel concerning the set of functions satisfying all the algebraic differential equations satisfied by a given function

http://dx.doi.org/10.4153/CMB-1998-031-0
Canad. Math. Bull. 41(1998), 214-224

  Published:1998-06-01
 Printed: Jun 1998

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.