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Homework Help: Bessel function derivative

  1. Jan 21, 2009 #1
    Hello,
    What is the value of the following derivavtive:
    [tex]\frac{d}{d\gamma}\left[ 1-\frac{2\gamma}{\sqrt{p}}e^{-\gamma \sigma/p} K_1\left(\frac{2\gamma}{\sqrt{p}} \right) \right][/tex]​
    where [tex]K_1(.)[/tex] is the modified Bessel function of the second kind and order 1?

    Some Paper shows that the result is:
    [tex]\frac{4\gamma}{p}e^{-\gamma\sigma/p}K_0\left(\frac{2\gamma}{\sqrt{p}}\right)+\frac{2\gamma\sigma}{p\sqrt{p}}e^{-\gamma\sigma/p}K_1\left(\frac{2\gamma}{\sqrt{p}}\right)[/tex]​

    But I really don't know how to connect them. The problem is how to handle the Bessel functions in the derivative operation? And what identity must use?

    Thanks in advance.
     
    Last edited: Jan 21, 2009
  2. jcsd
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