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Quadrature formulas for cauchy principal value integrals

Quadraturformeln für Cauchysche Hauptwertintegrale

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Abstract

Quadrature formulas of the Clenshaw-Curtis type, based on the “practical” abscissasx k=cos(kπ/n),k=0(1)n, are obtained for the numerical evaluation of Cauchy principal value integrals\(\int\limits_{ - 1}^1 {(x - a)^{ - 1} } f(x) dx, - 1< a< 1\).

Zusammenfassung

Die Quadraturformeln vom Clenshaw-Curtis Typ, die auf den “praktischen” Abszissenx k=cos(kπ/n),k=0(1)n, basieren, werden für die numerische Berechnung des Cauchyschen Hauptwerts\(\int\limits_{ - 1}^1 {(x - a)^{ - 1} } f(x) dx, - 1< a< 1\), abgeleitet.

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Chawla, M.M., Jayarajan, N. Quadrature formulas for cauchy principal value integrals. Computing 15, 347–355 (1975). https://doi.org/10.1007/BF02260318

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  • DOI: https://doi.org/10.1007/BF02260318

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