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Expansion Over a Rectangle of Real Functions in Bernoulli Polynomials and Applications

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Abstract

In this paper we generalize an expansion in Bernoulli polynomials for real functions possessing a sufficient number of derivatives. Starting from this expansion we obtain useful kernels, which are substantially different from Sard's for a wide class of linear functionals that includes the truncation error for cubature formulas.

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REFERENCES

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Authors and Affiliations

  1. Dipartimento di Matematica, Università della Calabria, Arcavacata, Rende, (CS), 87036, Italy

    F. A. Costabile & F. Dell'accio

Authors
  1. F. A. Costabile
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  2. F. Dell'accio
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Costabile, F.A., Dell'accio, F. Expansion Over a Rectangle of Real Functions in Bernoulli Polynomials and Applications. BIT Numerical Mathematics 41, 451–464 (2001). https://doi.org/10.1023/A:1021958910686

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  • DOI: https://doi.org/10.1023/A:1021958910686

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