Analytically Solving Bessel Functions for x Giving J_m(x)=0

[man@SUT]

If we want to find x giving J_m(x)=0 where m=any constants, how can we analytically get x?

Thank you

 

[mjsd]

I don't think you can do that analytically. (from memory)

 

[man@SUT]

I also use mathematica to solve but it doesn't help.

 

[siddharth]

You'll have an infinite number of real roots.

For large x, you can use the asymptotic formula for $$J_n(x)$$. If I remember right, the difference between successive roots will tend to $\pi$ for large x.

Alternatively, you could look up tables which give the zeros for various Bessel functions in a mathematical handbook

 

[man@SUT]

There will be the analytic solution when we assume x -> infinity or x<<1. In the case of the first few values of x giving J_m(x)=0, we might have to use the table to be the last choice. Anyway, thanks mjsd and siddharth.