Timeline for Legendre differential equation with additional term
Current License: CC BY-SA 3.0
14 events
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| Oct 11, 2014 at 12:05 | history | edited | Wolfgang |
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| Jun 10, 2014 at 15:54 | vote | accept | CommunityBot | ||
| Jun 9, 2014 at 12:16 | history | edited | user37929 | CC BY-SA 3.0 |
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| Jun 9, 2014 at 10:46 | history | edited | user37929 | CC BY-SA 3.0 |
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| Jun 9, 2014 at 3:41 | answer | added | Robert Israel | timeline score: 2 | |
| Jun 9, 2014 at 3:06 | comment | added | Igor Khavkine | Downvote. Your question is not a good fit for a research site. What you need some basic textbook knowledge about ODE and Sturm-Liouville theory, like Coddington & Levinson. | |
| Jun 9, 2014 at 1:54 | comment | added | Igor Khavkine | (1) The coefficients of the powers of $x$ will depend on $C$. (2) CASs know how to expand special functions in series. It is not magic, they apply the method of solution by series to the corresponding ODE. | |
| Jun 9, 2014 at 1:38 | history | edited | user37929 | CC BY-SA 3.0 |
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| Jun 9, 2014 at 1:33 | comment | added | Igor Khavkine | I think you've just restated the observation that representing the solution as a power series in $x$ will not determine which values of $C$ are eigenvalues. Beyond that, I can only reiterate the simple truth that every student of differential equations should know: it is unrealistic to expect to find solutions of a generic ODE without some kind of approximation. If you insist on no approximation, I don't know what else to tell you. | |
| Jun 9, 2014 at 0:44 | comment | added | Igor Khavkine | If you ask Maple to expand the Heun function in Series, it will be happy to oblige. So this representation of the solution should be explicit enough by your definition. On the other hand, a series expansion at $x=0$ or $x=1$ or $x=-1$ will not tell you anything about eigenvalues. Your best bet is probably numerics for now values of $C$ and a WKB approximation for large values of $C$. | |
| Jun 8, 2014 at 21:56 | history | edited | user37929 | CC BY-SA 3.0 |
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| Jun 8, 2014 at 21:28 | comment | added | Igor Khavkine | Could you make it clear, what "solutions" are you looking for? Do you want to find the eigenvalues $C$ (perhaps together with eigenfunctions)? If so, what boundary conditions are you taking? And what limits, if any, do you care about if explicit solutions are not available? | |
| Jun 8, 2014 at 21:08 | history | edited | user37929 | CC BY-SA 3.0 |
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| Jun 8, 2014 at 20:49 | history | asked | user37929 | CC BY-SA 3.0 |