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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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