高阶奇异积分求积公式的收敛性

高阶奇异积分求积公式的收敛性 ON THE CONVERGENCE OF QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF HIGHER ORDER 杜金元 Du Jinyuan first-author 本文建立了关于高阶奇异积分的机械求积公式在函数族D m-1 [a,b]上的一个收敛性定理,即定理2。它包含R.K.Miller关于广义积分的求积公式的收敛性结果作为特例。文中还对作者在[1] 中建立的Hunter型求积公式稍加变形,得到了修正形式的求积公式,将定理2应用于这种求积公式,得到了定理4,它包含D.Elliott关于Cauchy主值积分的求积公式的收敛性的结果作为其特例。 In this paper, A theorem on convergence of the mechanical quadrature formulae for singular integrals of higher order is established for the funct-ion family D m-1 [a, b], which includes R.K. Miller’s result about convergence of quadrature formulae for generalized integrals in [10] . Modifying slightly Hunter type quadrature formulae derived in [1] and at’plying this theorem to the modified quadrature formulae, we obtain a theorem for convergence of those modified quadrature formulae on D m-1 [a, b] which includes D. Elliottls result in [11] as a special case （m-1） since H[a, b] is a proper Subfamily of D[α, b] . 中国科学院科学基金 1984-02-01 2021-04-01 2