Approximation Theory and its Applications

, Volume 14, Issue 3, pp 106–116 | Cite as

Asymptotic approximation with Kantorovich polynomial



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\(\tfrac{d}{{dx}}K_n (f;x) - f'(x)\).


Asymptotic Expansion Asymptotic Approximation Simultaneous Approximation Polynomial Identity Central Moment 
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Copyright information

© Springer 1998

Authors and Affiliations

  1. 1.Fachhochschule Giessen-FriedbergFachbereich MNDFriedbergGermany

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