# nLab Schwarzian derivative

## Definition

The Schwarzian derivative is an operator on complex functions that is invariant under fractional linear transformations:

$(S f)(z) := \left( \frac{f''(z)}{f'(z)}\right)^' - \, \frac{1}{2} \left( \frac{f''(z)}{f'(z)}\right)^2 = \frac{f'''(z)}{f'(z)} - \frac{3}{2}\left( \frac{f''(z)}{f'(z)}\right)^2$

In fact the Schwarzian derivative of a fractional linear transformation, considered as a function from $\mathbb{C}$ to $\mathbb{C}$, is zero.

## References

category: analysis

Last revised on November 12, 2018 at 13:46:56. See the history of this page for a list of all contributions to it.