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1. CMB 1998 (vol 41 pp. 214)

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

Categories:34A34, 12H05

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