I have been trying to code an algorithm but I have faced the following problem about the second integral of modified Bessel function $ k_o(z)$ can you please help ;
In the paper there is an approximation for second integral of $ k_o(z)$ defined as ;
$\lim_{x\to0} k_2(x) = 1-\frac{pi}{2}*x+(\frac{3}{2}-ln\{\frac{e ^ {\gamma}}{2}-ln(x))*\frac{x^2}{2}$
I do not know how this approximation was derived and also since the above formula is only the limit for $ k_2(z)$ I want to know what is the complete form of the approximation of second internal of modified bessel function to use it in my code . Or do you think it is correct to use the equation above?
Please note that in the paper the first integral of modified bessel function $ k_o(z)$ is defined as
$ k_1(z)=\int_{x}^{\infty} k_0(z) dz$
and $ k_2(z)$ is defined as second integrtal of $ k_o(z)$ from x to $\infty$.
can some one please help as I have spent too much time on that with no result.
Thanks , Ehsan