Chebyshev series expansion of inverse polynomials

The Chebyshev series expansion of the inverse of a polynomial is well defined if the polynomial has no roots in [-1,1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. Also, if the first k of the coefficients an are known, the others become linear combinations of these derived recursively from the bj's. On a closely related theme, finding a polynomial with minimum relative error towards a given f(x) is approximately equivalent to finding the bj in ; a Newton algorithm produces these if the Chebyshev expansion of f(x) is known.