Geodesic
The growth of solutions of algebraic differential equations
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 2, pp. 67-73.

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Suppose that \( f(z) \) is a meromorphic or entire function satisfying \( P(z, f, f', \ldots , f^{(n)}) = 0 \) where \( P \) is a polynomial in all its arguments. Is there a limitation on the growth of \( f \), as measured by its characteristic \( T(r, f) \)? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given.
Sia \( f(z) \) una funzione meromorfa o intera dell'equazione \( P(z, f, f', \ldots , f^{(n)}) = 0 \), dove \( P \) è un polinomio in tutti i suoi termini. Esiste una limitazione della crescita di \( f \), considerata rispetto alla sua caratteristica \( T(r, f) \)? La risposta a tale questione non è in generale nota. L'autore e i Teoremi Gol'dberg e Steinmetz danno una risposta positiva in alcuni casi. Vengono anche forniti alcuni esempi. 
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Hayman, Walter K. The growth of solutions of algebraic differential equations. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 2, pp. 67-73. https://geodesic-test.mathdoc.fr/item/RLIN_1996_9_7_2_a1/

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