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:

$\displaystyle J_{1}(a\alpha _{n})Y_{0}(b\alpha _{n})-Y_{1}(a\alpha _{n})J_{0}(b\alpha _{n})=0$

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

$\displaystyle J_{0}(a\alpha _{n})Y_{0}(b\alpha _{n})-J_{0}(b\alpha _{n})Y_{0}(a\alpha _{n})=0$

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 :)

Re: Positive roots of functions using Bessel functions

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