On a linear homogeneous differential equation of Chebyshev type (Q2811577)
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scientific article; zbMATH DE number 6592204
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a linear homogeneous differential equation of Chebyshev type |
scientific article; zbMATH DE number 6592204 |
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10 June 2016
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differential equations
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Chebyshev system
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analytic functions
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0.9072695
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0.9009509
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0.8985114
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On a linear homogeneous differential equation of Chebyshev type (English)
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Consider the linear differential equation NEWLINE\[NEWLINEy^{(n)}(z)+ g_{n-1}(z)y^{(n-1)}(z)+\cdots+ g_1(z)y'(z)+ g_0(z)y(z)= 0,\tag{1}NEWLINE\]NEWLINE where all coefficients are analytic in \(|z|<R\). NEWLINEEquation (1) is called of Chebyshev type, if any solution of (1) not identically zero has at most \(n-1\) zeros. The author derives conditions on the functions \(g_k(z)\) such that (1) is of Chebyshev type.
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