# Chebyshev series expansion of inverse polynomials

@article{Mathar2006ChebyshevSE, title={Chebyshev series expansion of inverse polynomials}, author={R. Mathar}, journal={Journal of Computational and Applied Mathematics}, year={2006}, volume={196}, pages={596-607} }

The Chebyshev series expansion Σn=0∞anTn(x) of the inverse of a polynomial Σj=0kbjTj(x) 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… Expand

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