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Search: MSC category 12H05 ( Differential algebra [See also 13Nxx] )

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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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