Numerical integration in the presence of an interior singularity (Q1092351)

This paper is one of a series of investigations by the author on numerical integration when the integrand has a singularity in the interval. He first summarizes the previous results. His method is the Gauss-Jordan rule based on the zeros of the function \((1-x^ 2)P_{n- 2m}^{(\alpha,\beta)}(x),\) \(m=0,1\) where \(\alpha\) and \(\beta\) satisfy \(- \leq \alpha,\beta \leq\) or \(-1<\alpha =\beta\). He then discusses interpolatory integration rules and finally applies his methods to the study of convergence of the methods of \textit{D. B. Hunter} [Numer. Math. 19, 419-424 (1972; Zbl 0231.65028)] for Cauchy principal value integrals.