On generalizations of Ostrowski inequality via Euler harmonic identities (Q1869594)
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scientific article; zbMATH DE number 1902231
| Language | Label | Description | Also known as |
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| English | On generalizations of Ostrowski inequality via Euler harmonic identities |
scientific article; zbMATH DE number 1902231 |
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On generalizations of Ostrowski inequality via Euler harmonic identities (English)
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24 August 2003
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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.
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Ostrowski inequality
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harmonic polynomials
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generalized Euler-MacLaurin formula
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