Geodesic
Reprint: Über die Dezimalbruchentwicklung gewisser Irrationalzahlen (1937)
Documenta mathematica, Mahler Selecta (2019), pp. 459-474.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $(n)_q$ denote the base-$q$ expansion of the integer $n$. The Champernowne number to the base $q$ is the concatenation of the base-$q$ expansions of the positive integers after a radix point; that is, the number
$0.(1)_q(2)_q(3)_q\cdots(n)_q\cdots. $
In this paper, Mahler shows that each of these numbers is transcendental, but is not a Liouville number. \par Reprint of the author's paper [Mathematica B, Zutphen 6, 22--36 (1937; Zbl 0018.11102; JFM 63.0155.03)].
Classification : 11-03, 11J81, 11J91 
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     author = {Mahler, Kurt},
     title = {Reprint: {\"Uber} die {Dezimalbruchentwicklung} gewisser {Irrationalzahlen} (1937)},
     journal = {Documenta mathematica},
     pages = {459--474},
     publisher = {mathdoc},
     volume = {Mahler Selecta},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a25/}
}
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Mahler, Kurt. Reprint: Über die Dezimalbruchentwicklung gewisser Irrationalzahlen (1937). Documenta mathematica, Mahler Selecta (2019), pp. 459-474. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a25/