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Asymptotic approximation with Kantorovich polynomial

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Approximation Theory and its Applications

Abstract

We present the complete asymptotic expansion for the Kantorovich polynomials Kn as n→∞. The result is in a form convenient for applications. All coefficients of n−k (k=1,2,...) are calculated explicitly in terms of Stirling numbers of the first and second kind.

Moreover, we treat the simultaneous approximation with Kantorovich polynomials and determine the rate of convergence of\(\tfrac{d}{{dx}}K_n (f;x) - f'(x)\).

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Authors and Affiliations

  1. Fachhochschule Giessen-Friedberg, Fachbereich MND, Wilhelm-Leuschner-Strasse 13, D-61169, Friedberg, Germany

    Ulrich Abel

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  1. Ulrich Abel
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Correspondence to Ulrich Abel.

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Abel, U. Asymptotic approximation with Kantorovich polynomial. Approx. Theory & its Appl. 14, 106–116 (1998). https://doi.org/10.1007/BF02836771

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  • DOI: https://doi.org/10.1007/BF02836771

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