Liouville-Green-Olver approximations for complex difference equations (Q1283905)
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scientific article; zbMATH DE number 1271294
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Liouville-Green-Olver approximations for complex difference equations |
scientific article; zbMATH DE number 1271294 |
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Liouville-Green-Olver approximations for complex difference equations (English)
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19 August 1999
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The authors obtain the Liouville-Green-Olver approximations for second-order linear difference equations with complex coefficients, viz., \[ \Delta^2 y_n+ (a+g_n)y_n= 0, \] when \(a\in \mathbb{C}\setminus (0,+\infty)\neq -1\) and \(\sum_{n=\nu}^\infty | g_n|< \infty\). Second-order asymptotics with bounds is also obtained. The special case of ultraspherical functions of the second kind is discussed in detail.
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Liouville-Green-Olver approximations
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second-order linear difference equations
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complex coefficients
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asymptotics
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ultraspherical functions
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