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The Derivative of Bessel Function of the Second Kind

  1. Jul 24, 2009 #1

    What is [tex]\frac{d}{dx}K_v\left(f(x)\right)=?[/tex]

    Thanks in advance
  2. jcsd
  3. Jul 24, 2009 #2


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    For [itex]\nu[/itex] not necessarily an integer, [itex]C_{\nu}(y) = e^{\nu \pi i}K_{\nu}(y)[/itex] satisfies the identity

    [tex]2\frac{dC_\nu}{dy} = C_{\nu-1}(y) + C_{\nu + 1}(y)[/tex]

    Then let [itex]y = f(x)[/itex] and use the chain rule.

    Identities like this can usually be found on wikipedia, and for something as studied and used as frequently as the Bessel Functions, are generally correct.


    For a more 'official' reference, see something like http://www.math.sfu.ca/~cbm/aands/page_437.htm (scans of a reference book).
  4. Jul 24, 2009 #3
    I know that
    but I was confused when we have more complicated arguments such as
    But after your posting, I have now a simple method to move from simple to more complicated arguments. So, I can say the following:


    Am I right?

    Best regards
  5. Jul 27, 2010 #4
    Do you get the answer?
  6. Jul 27, 2010 #5
    let [tex]y=f(x)[/tex] and then use the chain rule.
  7. Jul 27, 2010 #6
    i think this is right
  8. Jul 27, 2010 #7
    thanks a lot
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