Timeline for Gegenbauer's addition theorem for Jacobi polynomials
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2021 at 5:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 6, 2021 at 5:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 19, 2019 at 15:06 | answer | added | Josiah Park | timeline score: 1 | |
| Dec 19, 2019 at 14:38 | history | edited | user114668 | CC BY-SA 4.0 |
updated with partial results
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| Dec 19, 2019 at 14:30 | history | edited | user114668 | CC BY-SA 4.0 |
updated with partial results
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| Dec 18, 2019 at 11:19 | comment | added | user114668 | A deleted answer showed the first result straightforwardly via the addition theorem DLMF (10.60.2) / (10.23.8). The first result can of course be ``naturally'' generalised by expressing one set of polynomials in terms of the other, but that does not lead to a final result which factorises in the same way. | |
| Dec 17, 2019 at 20:02 | comment | added | Nemo | This is direct consequence of partial wave expansion of $\frac{\sin R}{R}$, where $R=\sqrt{x^2+y^2-2xr\cos\theta}$. I think it might be found in Morse-Feshbach textbook. But I doubt it can be generalized for Jacobi polynomials instead of Legendre polynomials. | |
| Dec 17, 2019 at 20:01 | comment | added | Carlo Beenakker | for reference, the second integral evaluates for $n=\alpha=\beta=1$ to $\frac{8}{x^4 y^4} \sin y \left(x^3 y^2 \cos x-3 x^3 \cos x-7 x^2 y^2 \sin x+18 x^2 \sin x+18 y^2 \sin x-18 x y^2 \cos x-45 \sin x+45 x \cos x\right)+$ $\frac{8}{x^4 y^3} \cos y \left(3 x^3 \cos x+x^2 y^2 \sin x-18 x^2 \sin x-3 y^2 \sin x+3 x y^2 \cos x+45 \sin x-45 x \cos x\right)$. | |
| Dec 17, 2019 at 18:10 | review | First posts | |||
| Dec 17, 2019 at 20:05 | |||||
| Dec 17, 2019 at 18:07 | history | asked | user114668 | CC BY-SA 4.0 |