On interpolation and the Kimura-Georgiou parametrization

We show how the Kimura-Georgiou parametrization for interpolating a function and its derivatives at 0 is independent of the particular choice of basis of Szegö-polynomials of first and second kind, but only on the map between these two polynomial bases. This leads to a more general parametrization, which extends to different interpolation points and multivariable setup.