Solution of a second-order Poincaré-Perron-type equation and differential equations that can be reduced to it
The analytical solution of the second-order difference Poincare–Perron equation is presented. This enables us to construct in the explicit form a solution of the differential equation $$t^2(A_1t^2 + B_1t + C_1)u'' + t(A_2t^2 + B_2t + C_2)u' + (A_3t^2 + B_3t...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2008
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3208 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | The analytical solution of the second-order difference Poincare–Perron equation is presented.
This enables us to construct in the explicit form a solution of the differential equation
$$t^2(A_1t^2 + B_1t + C_1)u'' + t(A_2t^2 + B_2t + C_2)u' + (A_3t^2 + B_3t + C_3)u = 0 $$
The solution of the equation is represented in terms of two hypergeometric functions and one new special function.
As a separate case, the explicit solution of the Heun equation is obtained, and polynomial solutions of this equation are found. |
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