I need to calculate $\frac{\partial}{\partial\theta}J_0^2(\theta)$, where $J_0(\theta)$ is the modified Bessel function of the first kind and of zeroth order. Actually I need the roots of $J_0^2(\theta)=0$ and hence the derivative is required. Can anyone be of help?
Asked
Active
Viewed 154 times
0
-
the derivative is simply $-2 J_0(x)J_1(x)$ – tired Oct 28 '16 at 10:23
-
That I know, but what I'm unaware of is that if there exist any closed form expression of the roots of $J_0^2(\theta)$. – Priyadarshi Mukherjee Oct 28 '16 at 10:30
-
1There are no closed form expressions. Only very good approximations... – Jean Marie Oct 28 '16 at 11:20
-
That'll also serve the purpose... please do give some suitable references. – Priyadarshi Mukherjee Oct 28 '16 at 11:28
-
You can google for 'roots of bessel functions' to find many resources. Also, there is a nice calculator here: http://keisan.casio.com/exec/system/1180573472 – jcandy Oct 19 '17 at 02:17