Schwarzian Derivative - Definition

Definition

The Schwarzian derivative of a function of one complex variable ƒ is defined by

\begin{align} (Sf)(z) & = \left({f''(z) \over f'(z)}\right)' - {1\over 2}\left({f''(z)\over f'(z)}\right)^2 \\ & = {f'''(z) \over f'(z)}-{3\over 2}\left({f''(z)\over f'(z)}\right)^2. \end{align}

The alternative notation

is frequently used.

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