Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Gauss-Chebyshev quadrature formulae for strongly singular integrals


Author: Alexander M. Korsunsky
Journal: Quart. Appl. Math. 56 (1998), 461-472
MSC: Primary 65D32
DOI: https://doi.org/10.1090/qam/1637040
MathSciNet review: MR1637040
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Abstract: This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. The quadrature formulae are derived from those for Cauchy singular integrals.


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DOI: https://doi.org/10.1090/qam/1637040
Article copyright: © Copyright 1998 American Mathematical Society


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