Orders of solutions of an \(n\)-th order linear differential equation with entire coefficients (Q2742800)
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scientific article; zbMATH DE number 1650762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orders of solutions of an \(n\)-th order linear differential equation with entire coefficients |
scientific article; zbMATH DE number 1650762 |
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24 September 2001
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order of growth
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0.9395169
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0.93885565
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Orders of solutions of an \(n\)-th order linear differential equation with entire coefficients (English)
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This paper offers two sectorial type conditions which imply that all nontrivial solutions of the complex linear differential equation \(f^{(n)}+A_{n-1}(z)f^{(n-1)}+\cdots+ A_{1}(z)f'+A_{0}(z)f=0\) with entire coefficients, \(A_{0}(z)\not\equiv 0\), are of infinite order of growth. These results are straightforward generalizations of the corresponding results in the case \(n=2\) due to \textit{G. Gundersen} in [Trans. Am. Math. Soc. 305, 415--429 (1988; Zbl 0634.34004)]. The proofs offered are immediate adaptions of those given by Gundersen.
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