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# Numerical Evaluation of Cauchy Principal Value Integrals with Singular Integrands

Philip Rabinowitz
Mathematics of Computation
Vol. 55, No. 191 (Jul., 1990), pp. 265-276
DOI: 10.2307/2008804
Stable URL: http://www.jstor.org/stable/2008804
Page Count: 12
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## Abstract

Convergence results are proved for sequences of interpolatory integration rules for Cauchy principal value integrals of the form $$\not{\int}^1_{-1} k(x)(f(x)/(x - \lambda))dx,\quad -1 < \lambda < 1,$$ when $f(x)$ is singular at a point $\xi \neq \lambda$ and the singularity is ignored or avoided.

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