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Neumann Functions

  1. Feb 7, 2008 #1
    So for an assignment I have to write a program to find the roots of the Neumann function [tex]N_{n}(x)[/tex]. However the only Neumann function I have in my class notes is:
    Which is not overly helpful, and its the only one that was "boxed" in class.

    Any hints on how I can incorporate that into a computer program to find the roots would be great!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 7, 2008 #2


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    What system are you using to write the program? If it's something like Mathematica you should find that the Neumann function is already defined (as a form of Bessel function).
  4. Feb 7, 2008 #3
    I've never used Mathematica, though there seems to be a lot of people mentioning it. The prof wants us to use either C/C++ or FORTRAN. I have some experience with C++ so thats what I would be using.
    Also I would be compiling it in Unix/Linux, if that helps...

    Found an equation on Wikipedia:

    [tex]Y_{\alpha} = \frac{J_{\alpha}cos(\alpha \pi) - J_{- \alpha}}{sin(\alpha \pi)}[/tex]

    This one seems more promising, but not sure how to use it to find the first five roots for [tex]N_{1}[/tex], [tex]N_{2}[/tex], and [tex]N_{3}[/tex]
  5. Feb 7, 2008 #4


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    You should find built in functions in the C math libraries, things like jn and yn. Setting up decent approximations for transcendental functions like this is a job for a numerical analysis type person. Just finding roots once the functions are defined isn't so hard.
  6. Feb 7, 2008 #5
    Sounds doable.. will. report back with success or failure.
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