Geodesic
Analytic complexity of differential algebraic functions
Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1774-1787

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Examples of differential algebraic functions with infinite analytic complexity are constructed. The fact of their existence implies that the class of differential algebraic functions is wider than the class of functions with finite complexity. Bibliography: 6 titles.
Keywords: analytic complexity, differential algebraic functions. 
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     author = {M. A. Stepanova},
     title = {Analytic complexity of differential algebraic functions},
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M. A. Stepanova. Analytic complexity of differential algebraic functions. Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1774-1787. http://geodesic.mathdoc.fr/item/SM_2019_210_12_a5/