This article is cited in 1 paper

Quadrature processes for integrals of Cauchy type

D. G. Sanikidze

Computer Center, Academy of Sciences of the Georgian SSR

Abstract: We study questions relating to convergence of the process
$$ \int_{-1}^{+1}\rho(t)\frac{f(t)}{t-x}dt\approx\sum_{k=1}^n\alpha_{k,n}(x)f(x_k^{(n)})\qquad(-1<x<1), $$
wherein the singular integral is taken in the principal value sense. General conditions for convergence in the class of continuously differentiable functions $f$ are formulated. In the case of the weight function $\rho(t)=(\sqrt{1-t^2})^{-1}$, we investigate, under various assumptions on $f$, the convergence of a specific quadrature process.

UDC: 517.5

Received: 02.03.1970

 English version: Mathematical Notes, 1972, 11:5, 316–321

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