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Math Help - Positive roots of functions using Bessel functions

  1. #1
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    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:

    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:

    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
    Last edited by hannah89; January 1st 2013 at 06:32 PM. Reason: latex mixup
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  2. #2
    MHF Contributor
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    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
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