Euler-Maclaurin expansions for integrals with endpoint singularities: a new perspective

@article{Sidi2004EulerMaclaurinEF,
  title={Euler-Maclaurin expansions for integrals with endpoint singularities: a new perspective},
  author={Avram Sidi},
  journal={Numerische Mathematik},
  year={2004},
  volume={98},
  pages={371-387}
}
In this note, we provide a new perspective on Euler{Maclaurin expansions of (o set) trapezoidal rule approximations of the nite-range integrals I [f ] = R b a f(x) dx, where f 2 C1(a; b) but can have general algebraic-logarithmic singularities at one or both endpoints. These integrals may exist either as ordinary integrals or as Hadamard nite part integrals. We assume that f(x) has asymptotic expansions of the general forms f(x) 1 Xs=0 Ps(log(x a))(x a) s as x! a+; f(x) 1 Xs=0Qs(log(b x))(b x… CONTINUE READING

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