ASYMPTOTICALLY SHARP ERROR-ESTIMATES FOR MODIFIED COMPOUND QUADRATURE-FORMULAS FOR CAUCHY PRINCIPAL VALUE INTEGRALS

One of the standard methods for computing Cauchy principal value integ rals is to subtract the singularity, and then to apply a given quadrat ure formula. This results in a quadrature formula for the Cauchy princ ipal value integral which is called a modified quadrature formula. Her e, we consider the case that this given quadrature formula is a compou nd quadrature formula, and derive error estimates of the form \R[f]]le ss than or equal to kappa(i) parallel to f((i))parallel to(infinity)(w here R[f] is the error of the modified quadrature formula). In contras t to previous estimates, the behaviour of kappa(i) when the number of quadrature nodes tends to infinity is determined exactly.