Inverse Stieltjes Iterates and Errors of Pade Approximants in the Whole Complex-plane

Gilewicz, J.;Magnus, AP.
(1993) 7th Spanish Symposium on Orthogonal Polynomials and Applications ( VII SPOA ) — Location: GRANADA(Spain) (23.September.1991)

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  • Gilewicz, J.
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  • Magnus, AP.
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Abstract
The Stieltjes functions f and g, related by f(z) = f0(1 - zg(z))-1, are respectively developed in terminating continued C-fractions. Computing the last approximants of the two above C-fractions, we obtain, in the whole complex plane and for the whole Pade table, the exact relations between contiguous Pade approximants errors.
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Gilewicz, J., & Magnus, AP. (1993). Inverse Stieltjes Iterates and Errors of Pade Approximants in the Whole Complex-plane. Journal of Computational and Applied Mathematics, 49(1-3), 79-84. https://doi.org/10.1016/0377-0427(93)90137-Z (Original work published 1993)