Geodesic
Two remarks about Picard-Vessiot extensions and elementary functions
Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 173-183.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group $Gal_{L} M$ is a normal subgroup of $Gal_{K} M$. We also present a proof that the probability function Erf(x) is not an elementary function.
DOI : 10.4064/cm-84/85-1-173-183

Henryk Żołądek 1

1 
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Henryk Żołądek. Two remarks about Picard-Vessiot extensions and elementary functions. Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 173-183. doi : 10.4064/cm-84/85-1-173-183. http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-173-183/

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