Perturbed Generalised Taylor's Formulae with Sharp Bounds

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Cerone, Pietro (2002) Perturbed Generalised Taylor's Formulae with Sharp Bounds. RGMIA research report collection, 5 (2).

Abstract

Sharp bounds are obtained for perturbed generalised Taylor series. The perturbation involves the arithmetic sum of the upper and lower bounds of the (n + 1)th derivative. The sharpest bound is in terms of the one norm of the Appell polynomial which constitutes the coefficients of the derivative of the function to be approximated. The results are demonstrated for an application to the logarithm.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17711
Subjects Current > FOR Classification > 0102 Applied Mathematics
Current > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords perturbed generalised Taylor’s formula, Appell polynomials, Sharp bounds, Čebyšev-type functional
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