In this paper, we consider a quadrature rule for Cauchy integrals of the form I(wf: s)= integral (1)(-1) w(t) f(t) (t - s) dt. -1 < s < 1. for smooth density function f(t) and Jacobi's weights w(t)=( I t)(x) (1 + t)(beta), x, beta> 1 2. Using the change of variables t = cos y, s = cos x and subtracting out the singularity, we propose a trigonometric quadrature rule. We obtain the error bounds independent of the set of values of poles and construct an automatic quadrature of nonadaptive type. (C) 2001 Academic Press. [References: 18]
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机译：在本文中，我们考虑形式为I（wf：s）=积分（1）（-1）w（t）f（t）（t-s）dt的柯西积分的正交规则。 -1 1 2.使用变量t = cos y，s = cos x并减去奇点，我们提出了一个三角正交规则。我们获得独立于极点值集的误差范围，并构造了非自适应类型的自动正交。 （C）2001学术出版社。 [参考：18]
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