K ν ⁡ ( z ) ∼ ( π 2 ⁢ z ) 1 2 ⁢ e − z ⁢ ∑ k = 0 ∞ a k ⁡ ( ν ) z k K_{\nu }\left(z\right)\sim \left({\frac {\pi }{2z}}\right)^{\frac {1}{2}}e^{-z}\sum _{k=0}^{\infty }{\frac {a_{k}(\nu )}{z^{k}}}