Summary
For functions with an interior singularity, the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler ‘Euler-Maclaurin type formulae’. Applying this method to certain classes of functions, such as, for example,f(x)=h(x)|x-u| β, where β>−1, with a sufficiently smooth functionh, we obtain the main term of the error expansion for quadrature rules of ultraspherical type.
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Petras, K. Asymptotics for the remainder of a class of positive quadratures for integrands with an interior singularity. Numer. Math. 65, 121–133 (1993). https://doi.org/10.1007/BF01385744
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DOI: https://doi.org/10.1007/BF01385744