Thread: Positive roots of functions using Bessel functions

Hi there,

This is my first time using latex too, so I hope that works

I am trying to use an expression that requires me to find the positive roots to:




Now, I have found a table which gives the roots of:



for various b/a values.

My question is: does anyone know where to find more tables for other expressions, or - can anyone point me in the right direction for how to find the roots? I had previously posted a similar question but now I think I understand a little more what i'm doing so I've written a new post. I'm basically quite lost and so any help would be greatly appreciated.

Thanks in advance

Code:

a = 1;
b = 2;
zeros = Quiet[
   Table[FindRoot[
     BesselJ[0, a*x]*BesselY[0, b*x] - 
       BesselJ[0, b*x]*BesselY[0, a*x] == 0, {x, n*Pi - .1}], {n, 1, 
     100}]];
g = x /. zeros;
g // TableForm

Mathematica: first 100 zeros