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Abstract
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< s <1, for a smooth density function f ( t ) and Jacobi's weights w ( t )=(1− t ) α (1+ t ) β , α , β >−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.
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