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The Euler-Maclaurin Formula in Presence of a Logarithmic Singularity

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Abstract

In this short note we prove an extension of the Euler-Maclaurin expansion for general rectangular composite quadrature rules in one dimension when the derivative of the integrand has a logarithmic singularity. We show that a correction series has to be added to the formula, but that the asymptotic expansion in powers of the discretization parameter still holds.

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Authors and Affiliations

  1. Departamento Matemática Aplicada-E.U.I.T.I.Z, Universidad de Zaragoza-Corona de Aragón, 50009, Zaragoza, Spain. email: celorrio@posta.unizar.es

    Ricardo Celorrio

  2. Departamento Matemática Aplicada-Centro Politécnico Superior, Universidad de Zaragoza-María de Luna, 3, 50015, Zaragoza, Spain. e-mail: jsayas@posta.unizar.es

    Francisco-Javier Sayas

Authors
  1. Ricardo Celorrio
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  2. Francisco-Javier Sayas
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Celorrio, R., Sayas, FJ. The Euler-Maclaurin Formula in Presence of a Logarithmic Singularity. BIT Numerical Mathematics 39, 780–785 (1999). https://doi.org/10.1023/A:1022399409604

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  • DOI: https://doi.org/10.1023/A:1022399409604

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