In my version of Schaums mathematical handbook (4th edition page 156), it gives the following for $K_0$
$$ K_0= -\big(ln(x/2)+\gamma\Big) I_0(x)+\frac{x^2}{2}+\frac{x^4}{2^2\cdot4^2}\left(1+\frac{1}{2}\right)+\frac{x^6}{2^2\cdot4^2\cdot6^2}\left(1+\frac{1}{2}+\frac{1}{3}\right)+... $$
But it doesn't define what $\gamma$ is.
Is $\gamma$ some arbitrary constant?
$\gamma$ is the Euler-Mascheroni constant.