A Trigonometric Quadrature Rule for Cauchy Integrals with Jacobi Weight Original Research Article

In this paper, we consider a quadrature rule for Cauchy integrals of the form I(wf; s)=[formula] w(t) f(t)/(t−s) dt, −1−1/2. 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.