Schwarzian Derivative

$(Sf)(z)\; =\; \{f$'(z) \over f'(z)}-{3\over 2}\left({f(z)\over f'(z)}\right)^2.

$g(z)=(az+b)/(cz+d)$

$(S(f\backslash circ\; g))(z)=g\text{'}(z)^2(Sf)(g(z)).$

$(Sf)(y)=6\backslash lim\_\{x\backslash rightarrow\; y\}\; \backslash left(\{f\text{'}(x)f\text{'}(y)\backslash over(f(x)-f(y))^2\}-\{1\backslash over(x-y)^2\}\backslash right).$

References

• V. Ovsienko, S. Tabachnikov : Projective Differential Geometry Old and New, Cambridge University Press, 2005. ISBN 0521831865 .

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