Solution of a second-order linear differential equation with polynomial coefficients and Fuchsian point at zero (Q542151)
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scientific article; zbMATH DE number 5905367
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solution of a second-order linear differential equation with polynomial coefficients and Fuchsian point at zero |
scientific article; zbMATH DE number 5905367 |
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Solution of a second-order linear differential equation with polynomial coefficients and Fuchsian point at zero (English)
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8 June 2011
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The author considers the differential equation \[ z^2Py''+zP_1y'+P_2y=0,\tag{1} \] where \(P,P_1,P_2\in \mathbb{C}[z]\), \(\text{deg}P_1=2\text{deg}P\), \(\text{deg}P_2=3\text{deg}P\) and \(P(0)\neq 0\). When equation (1) has a fundamental system of solutions in \(\mathbb{C}\{z^{q^{-1}}\}\), the author constructs solutions via fractional-order hypergeometric functions.
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second-order linear differential equation
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