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2004•Unpublished venueRequires access

On the Integrals of Rational Functions When Having Pole in the Real Axis and Their Cauchy Principal Value

Zhirong Li

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Abstract

Based on the weakening term of the integral complex analysis, this paper discusses abnormal integrals of the rational function R(z) without pole in the semi-real axis x≥0; also discusses the Cauchy principal value(P. V. ) of the abnormal integrals when R(z) only has pole z = 1 in the semi-real axis x≥ 0; further,presents the theorem of relational expression between R(x)dx (or the Cauchy principal value) and the residues.

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What this paper is about

Based on the weakening term of the integral complex analysis, this paper discusses abnormal integrals of the rational function R(z) without pole in the semi-real axis x≥0; also discusses the Cauchy principal value(P. V. ) of the abnormal integrals when R(z) only has pole z = 1 in the semi-real axis x≥ 0; further,presents the theorem of relational expression between R(x)dx (or the Cauchy principal value) and the residues.

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Available abstract

Based on the weakening term of the integral complex analysis, this paper discusses abnormal integrals of the rational function R(z) without pole in the semi-real axis x≥0; also discusses the Cauchy principal value(P. V. ) of the abnormal integrals when R(z) only has pole z = 1 in the semi-real axis x≥ 0; further,presents the theorem of relational expression between R(x)dx (or the Cauchy principal value) and the residues.

Key concepts: Cauchy principal value, Principal value, Mathematics, Cauchy's integral formula, Cauchy's integral theorem, Cauchy distribution, Value (mathematics), Principal (computer security)

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