Geodesic
On a Problem of Rubel Concerning the Set of Functions Satisfying All the Algebraic Differential Equations Satisfied by a Given Function
Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 214-224

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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.
DOI : 10.4153/CMB-1998-031-0
Mots-clés : 34A34, 12H05 
Shackell, John. On a Problem of Rubel Concerning the Set of Functions Satisfying All the Algebraic Differential Equations Satisfied by a Given Function. Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 214-224. doi: 10.4153/CMB-1998-031-0
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     title = {On a {Problem} of {Rubel} {Concerning} the {Set} of {Functions} {Satisfying} {All} the {Algebraic} {Differential} {Equations} {Satisfied} by a {Given} {Function}},
     journal = {Canadian mathematical bulletin},
     pages = {214--224},
     year = {1998},
     volume = {41},
     number = {2},
     doi = {10.4153/CMB-1998-031-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-031-0/}
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