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Mat. Zametki, 1972, Volume 11, Issue 5, Pages 517–526 (Mi mz9818)  

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.

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

Bibliographic databases:

UDC: 517.5
Received: 02.03.1970

Citation: D. G. Sanikidze, “Quadrature processes for integrals of Cauchy type”, Mat. Zametki, 11:5 (1972), 517–526; Math. Notes, 11:5 (1972), 316–321

Citation in format AMSBIB
\Bibitem{San72}
\by D.~G.~Sanikidze
\paper Quadrature processes for integrals of Cauchy type
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 5
\pages 517--526
\mathnet{http://mi.mathnet.ru/mz9818}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=304945}
\zmath{https://zbmath.org/?q=an:0246.41026|0234.41006}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 5
\pages 316--321
\crossref{https://doi.org/10.1007/BF01158644}


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