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Something about Bessel function

  1. Dec 6, 2009 #1
    I am working on some numerical works. I use the computer language: Fortran language.
    Here I have a problem about the Bessel functon.

    Now I know the value of Bessel[v,x], where v is positive and real.
    I want to know the value of Bessel[-v,x].

    I don't know their relation. Can you help me?
    Thanks!
     
  2. jcsd
  3. Dec 7, 2009 #2

    Born2bwire

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    The Bessel function satisfies the differential equation,

    [tex]x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - \nu^2)y = 0[/tex]

    We can see here that the sign of the order wold seem to be irrelevant because we take its square. However, the relationship is

    [tex]J_{-n}(x) = (-1)^nJ_n(x)[/tex]
     
  4. Dec 7, 2009 #3
    As far as I know, when n is integer, you are right: [tex]J_{-n}(x) = (-1)^nJ_n(x)[/tex].
    But when n is not integer, it becomes very difficult.
     
  5. Dec 7, 2009 #4

    Born2bwire

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

    via Numerical Recipes.
     
  6. Dec 22, 2009 #5
    You are very clever.
     
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