This circle has the equation x2 + y2 = 25, and it contains rational points, like (0, 5) and (3, 4), as well as other points, like (2, \sqrt {21}) and (\sqrt {11}, - \sqrt {14}). But knowing just one ...

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 ...

These results form the mathematical foundation of related spectral and pseudospectral methods for solving partial differential equations on the half line. A spectral scheme using the modified Legendre ...