Euler-Maclaurin expansions for integrals with endpoint singularities: a new perspective
نویسنده
چکیده
In this note, we provide a new perspective on Euler–Maclaurin expansions of (offset) trapezoidal rule approximations of the finite-range integrals I [f ] = ∫ b a f (x) dx, where f ∈ C∞(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 finite part integrals. We assume that f (x) has asymptotic expansions of the general forms
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ورودعنوان ژورنال:
- Numerische Mathematik
دوره 98 شماره
صفحات -
تاریخ انتشار 2004