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Expansion over a rectangle of real functions in Bernoulli polynomials and applications. (English) Zbl 0989.65014

A new expansion of a sufficiently smooth univariate real function in terms of Bernoulli polynomials has been given by F. Costabile [Conf. Sem. University Bari, N 273 (1999)]. The authors generalise this expansion for the bivariate case. Using this, some useful kernels are obtained which are substantially different from Sard kernel for a wide class of linear functional that includes the truncated error for cubature formulas.

MSC:

65D15 Algorithms for approximation of functions
65D32 Numerical quadrature and cubature formulas
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