Timeline for Closed form for the integral of a squared Legendre function
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2020 at 17:30 | comment | added | Michael Engelhardt | The measure seems odd - $\sin \theta d\theta $ would look a lot more natural. It might be useful to have more details on how this integral comes about. | |
| Jul 24, 2020 at 17:05 | answer | added | skbmoore | timeline score: 1 | |
| Jul 21, 2020 at 18:03 | history | edited | Max Alekseyev |
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| Jul 21, 2020 at 3:27 | comment | added | Max Alekseyev | Also, for integer parameters $\nu,\mu$, associated Legendre function $P_\nu^\mu(x)$ turns into the associated Legendre polynomial. However, such polynomial is zero when $\mu>\nu$. So, please clarify the meaning of $P_\nu^\mu(x)$ in your question. | |
| Jul 21, 2020 at 2:50 | comment | added | Max Alekseyev | Your link refers to formula 14.3.6, which holds for $x > 1$ (while $\cos\theta\leq 1$). Do you actually mean formula 14.3.1, that is Ferrers rather than Legendre functions? | |
| Jul 20, 2020 at 17:16 | comment | added | Timothy Budd | Using its recurrence formulas it boils down to evaluating the overlap $\int_{-1}^1P_{\nu}^\mu(x) P_{\nu-1}^{\mu\pm1}(x) \mathrm{d} x$ of two associated Legendre polynomials. Perhaps this source helps? | |
| Jul 20, 2020 at 10:27 | review | First posts | |||
| Jul 20, 2020 at 11:38 | |||||
| Jul 20, 2020 at 10:20 | history | asked | 西島晃彦 a.k.a. Teru-san | CC BY-SA 4.0 |