| 1. | Is there really no more subtelty beyond that of the power series?
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| 2. | A limitation of the power series solution shows itself in this example.
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| 3. | They have different power series depending on which point you expand about.
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| 4. | Some such differential equations admit explicit power series solutions, despite their non-linearity.
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| 5. | :What do you mean by " have a power series "?
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| 6. | For non-integer ?, a more general power series expansion is required.
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| 7. | The Legendre differential equation may be solved using the standard power series method.
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| 8. | A suitable truncation of the power series then yields a parametrix.
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| 9. | Moreover, there can be no other power series with this property.
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| 10. | Then the formal power series ring AX is completely integrally closed.
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