= Spherical derivative of a meromorphic function
{title2=$f^{\#}_{\mathrm{round}}=2|f'|/(1+|f|^2)$}
For a <meromorphic function> viewed as a <holomorphic map> to the unit <Riemann sphere>, this is the length density of the pulled-back spherical metric. Its square is the pulled-back area density. At a <pole> use the coordinate $1/f$, which gives the same density. Some conventions omit the factor two and use a sphere of area $\pi$; all area normalizations must then change accordingly.
Back to article page