Chebyshev Series Expansion of Inverse Polynomials

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. If the first k of the coefficients an are known, the others become linear combinations of these with expansion coefficients 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 f(x)/ ∑k 0 bjTj(x) = 1 + ∑ ∞ k+1 anTn(x), and may be handled with a Newton method providing the Chebyshev expansion of f(x) is known.