This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example, on the real line), then the function maps this circle into ...

Rhie also came up with an ingenious way of constructing an example of a rational harmonic function with exactly 5n - 5 zeros. Together with the result of Khavinson and Neumann, this example ...

We provide an algorithm to compute the nodes and weights for Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside [-1, 1]. Contrary ...