Timeline for Orthogonality of Bessel function $\int_0^bxJ_a(\ell x)J_a(\ell' x)=0$ for $\ell\neq\ell'$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2021 at 17:28 | vote | accept | CommunityBot | ||
| Jan 1, 2021 at 16:53 | answer | added | Alapan Das | timeline score: 0 | |
| Jan 1, 2021 at 16:51 | comment | added | user161698 | @ChristianRemling yes that is what I am asking--- how can I set it up? Thanks. | |
| Jan 1, 2021 at 16:50 | comment | added | user161698 | @AlapanDas $x^2y''+xy'+(\ell^2x^2-a^2)y=0$. Replace $y$ by $J_a(\ell x).$ | |
| Jan 1, 2021 at 16:50 | comment | added | Christian Remling | Eigenfunctions of a self-adjoint operator are orthogonal, so if you set it up correctly, you don't need any calculation. | |
| Jan 1, 2021 at 16:47 | comment | added | Alapan Das | The Bessel equation is $(xJ'_a(lx))'+(l^2x-\frac{q^2}{x})J_a(lx)=0$. | |
| Jan 1, 2021 at 16:39 | history | edited | user161698 | CC BY-SA 4.0 |
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| Jan 1, 2021 at 16:35 | comment | added | user161698 | Ahhh sorry that is a typo. | |
| Jan 1, 2021 at 16:33 | history | edited | user161698 | CC BY-SA 4.0 |
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| Jan 1, 2021 at 16:33 | comment | added | user161698 | @AlapanDas when you say "that" what do you mean? | |
| Jan 1, 2021 at 16:29 | answer | added | Gerald Edgar | timeline score: 0 | |
| Jan 1, 2021 at 16:18 | comment | added | user161698 | @AlapanDas Yes I changed $q$ to $a$. However changing $a$ to $m$ is unnecessary. I just used it as a dummy variable. | |
| Jan 1, 2021 at 16:17 | history | edited | user161698 | CC BY-SA 4.0 |
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| Jan 1, 2021 at 15:57 | history | asked | user161698 | CC BY-SA 4.0 |