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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

Published online by Cambridge University Press:  20 November 2018

John Shackell
John Shackell*
Affiliation:
Institute of Mathematics and Statistics The University Canterbury Kent CT2 7NF England, e-mail: J.R.Shackell@ukc.ac.uk
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Abstract

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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.

Keywords

34A3412H05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 2 , 01 June 1998 , pp. 214 - 224
Copyright
Copyright © Canadian Mathematical Society 1998

References

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4. van der Waerden, B. J., Algebra, vol.2. Frederick Ungar Pub. Co., 1950.Google Scholar