an:01902231
Zbl 1018.26015
Dedi??, Lj.; Mati??, M.; Pe??ari??, J.; Vukeli??, A.
On generalizations of Ostrowski inequality via Euler harmonic identities
EN
J. Inequal. Appl. 7, No. 6, 787-805 (2002).
00091549
2002
j
26D15 41A55
Ostrowski inequality; harmonic polynomials; generalized Euler-MacLaurin formula
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.
Kai Diethelm (Braunschweig)