This question is a continuation of the question posted here. The problem here is to solve the integral with modified Bessel function of second kind, $K_0\left(u\right)$:
$$F\left ( x \right )=\frac{2\beta }{\left ( \sigma \Gamma \left [ \frac{1}{\beta } \right ] \right )^{2}}\int_{0}^{x}K_{0}\left ( \frac{2t^{\frac{\beta }{2}}}{\sigma ^{\beta }} \right )dt$$
where $\beta, \sigma, x>0$ and $F(x)$ is the Cumulative Distribution Function (CDF) of a distribution
The main problem here is to solve
$$\int_{0}^{x}K_{0}\left ( \frac{2t^{\frac{\beta }{2}}}{\sigma ^{\beta }} \right )dt$$
I tried using guidance from here but no luck. How can this be solved? Thanks
Answer:
Follow @Lucian's comment below
