S_David
Jan21-09, 03:01 PM
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.
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.