\[Y_{0}\left(z\right)=\frac{2}{\pi}\left(\ln\left(\tfrac{1}{2}z\right)+\gamma%
\right)J_{0}\left(z\right)+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2%
}}-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+%
\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\dotsi\right),\]