If we want to find x giving J_m(x)=0 where m=any constants, how can we analytically get x?
I don't think you can do that analytically. (from memory)
I also use mathematica to solve but it doesn't help.
You'll have an infinite number of real roots.
For large x, you can use the asymptotic formula for [tex]J_n(x)[/tex]. If I remember right, the difference between successive roots will tend to [itex]\pi[/itex] for large x.
Alternatively, you could look up tables which give the zeros for various Bessel functions in a mathematical handbook
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.
Separate names with a comma.