# Bessel function derivative

1. Jan 21, 2009

### EngWiPy

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

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

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
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