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On generalizations of Ostrowski inequality via Euler harmonic identities. (English) Zbl 1018.26015
A sequence \((P_k)\) of polynomials is said to be harmonic if \(P_0= 1\) and \(P_k' = P_{k-1}\) for all \(k\). The authors prove a generalized version of the Euler-MacLaurin sum formula for the midpoint quadrature method, replacing the Bernoulli polynomials by an arbitrary harmonic sequence of polynomials. As a consequence, a generalized Ostrowski inequality is derived.

MSC:
26D15 Inequalities for sums, series and integrals
41A55 Approximate quadratures
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