The numerical evaluation of singular integrals with coth-kernel

Singular integrals with hyperbolic cotangent kernel present their own numerical problems because of the poles of the kernel located in the complex plane. We write such integrals as ordinary Cauchy principal value integrals involving an appropriate (nonclassical) weight function and apply quadrature methods of Gaussian and interpolatory type. The most accurate one is based on Gauss-Christoffel quadrature relative to the weight function in question. Its error is studied both by real-and complex-variable techniques. Numerical examples are given to illustrate the theory.The work of the first author was supported in part by the National Science Foundation under grant DCR-8320561.