@article{oai:u-fukui.repo.nii.ac.jp:02000112,
 author = {Hasegawa, Takemitsu and Sugiura, Hiroshi},
 journal = {Journal of Computational and Applied Mathematics},
 month = {Jan},
 note = {An approximation of Clenshaw–Curtis type is given for Cauchy principal value integrals of logarithmically singular functions I(f;c)=f^1_-1 f(x)(log | x－c) / (x－c) dx (c ∈(－1,1))  with a given function f. Using a polynomial  pN of degree N  interpolating f  at the Chebyshev nodes we obtain an approximation I(pN;c)≅I(f;c). We expand pN  in terms of Chebyshev polynomials with O(N log N) computations by using the fast Fourier transform. Our method is efficient for smooth functions f, for which pN  converges to f  fast as N  grows, and so simple to implement. This is achieved by exploiting three-term inhomogeneous recurrence relations in three stages to evaluate I(pN;c). For f(z) analytic on the interval ［－1,1］in the complex plane z, the error of the approximation  I(pN;c)  is shown to be bounded uniformly. Using numerical examples we demonstrate the performance of the present method.},
 pages = {1--11},
 title = {Uniform approximation to Cauchy principal value integrals with logarithmic singularity},
 volume = {327},
 year = {2018}
}