The Schwarzian derivative

The Schwarzian derivative of a function f is a rational function of the derivatives of f to order 3. In fact it can be expressed in terms of the logarithmic derivative \(f''/f'\) of \(f'\). Here we show that the Schwarzian derivative is a natural object: a measure of the “curvature” of f, the pointwise deviation from a best approximation of f by a linear fractional transformation.