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Peano kernels of non-integer order. (English) Zbl 0880.41022

Summary: 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.

MSC:

41A55 Approximate quadratures
26A33 Fractional derivatives and integrals
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