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Zeitschrift für Analysis und ihre Anwendungen

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Volume 16, Issue 3, 1997, pp. 727–738
DOI: 10.4171/ZAA/787

Published online: 1997-09-30

Peano Kernels of Non-Integer Order

K. Diethelm[1]

(1) Universität Hildesheim, Germany

We consider the representation of error functionals in numerical quadrature by the Peano kernel method. It is easily observed that the usual expressions for Peano kernels of order s still make sense if s is not a natural number. In this paper, we discuss how to interpret these Peano kernels, we state their main properties, and we compare them to the (classical) Peano kernels of integer order.

Keywords: Quadrature formulas, error bounds, Peano kernels, fractional calculus

Diethelm K.: Peano Kernels of Non-Integer Order. Z. Anal. Anwend. 16 (1997), 727-738. doi: 10.4171/ZAA/787