Some Results about Cauchy Improper Integral

Arwa

doi:https://doi.org/10.54216/GJMSA.010201

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Volume 1 • Issue 2 • PP: 08-10 • 2022

Some Results about Cauchy Improper Integral

Arwa Hajjari ^1*

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¹Cairo University, Cairo, Egypt

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.010201

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Received: January 10, 2022 Accepted: April 15, 2022

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Abstract

The objective of this paper is to estimate the value of∫_(-1)^1〖f(x)/(x-t)^m dx ;m∈N〗 where f is convex from above and ∫_0^δ〖w(f^((m-1) ),x)/x dx<∞; fis bounded in C^((m-1) ) [-1,1].

Keywords

Improper Integral Cauchy Principal value Convex function

References

[1] CAROTHERS.N. – A short course on Approximation Theory I Bowling Green state University

Math682Smmer 1998.

[2] KORNEUSHYK .N.B .EXat constant in approximation Theory.Nauka.Mosscow .p424 (in Russian)-1987.

[3] Chawla .,M.M.&Jayarajan ,.,Quadrature formolas for Cauchy principal value integrals ,computing ,15,347 -

355(1975).

[4] Das,R.N.&Hota.K.,A derivative free quadraturole for numerical approximations of complex Cauchy

principal value integrals ,Appl.Math.Sci.,69,5533-5540.(2012)

[5] Davis,P,J.&Robinowitz,P., Method of Numerical integration( nd (2 edn , Academic Prress,NY.1984,

[6] Diethelm,K., Gaussian quadrature formulas of the third kind for Cauchy principal value integrals :basic

properties and error estimates ;J.comp.Appl.Math .,65997114(1998)

[7] Hunter ,D.B, Some Gauss type formulae for the evolution of Cauchy principal values ointegrals,Numer Math

.419-4-8(1992)

[8] Milovanovic ,G.v.,Acharya ,B.P.&Pahana.K,I.N.,Some interpalated rule for the approximative evaluation of

complex CPV integrals Rev.Res.,14,89-100(1984)

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Hajjari, Arwa. "Some Results about Cauchy Improper Integral." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 1, no. Issue 2, 2022, pp. 08-10. DOI: https://doi.org/10.54216/GJMSA.010201

Hajjari, A. (2022). Some Results about Cauchy Improper Integral. Galoitica: Journal of Mathematical Structures and Applications, Volume 1(Issue 2), 08-10. DOI: https://doi.org/10.54216/GJMSA.010201

Hajjari, Arwa. "Some Results about Cauchy Improper Integral." Galoitica: Journal of Mathematical Structures and Applications Volume 1, no. Issue 2 (2022): 08-10. DOI: https://doi.org/10.54216/GJMSA.010201

Hajjari, A. (2022) 'Some Results about Cauchy Improper Integral', Galoitica: Journal of Mathematical Structures and Applications, Volume 1(Issue 2), pp. 08-10. DOI: https://doi.org/10.54216/GJMSA.010201

Hajjari A. Some Results about Cauchy Improper Integral. Galoitica: Journal of Mathematical Structures and Applications. 2022;Volume 1(Issue 2):08-10. DOI: https://doi.org/10.54216/GJMSA.010201

A. Hajjari, "Some Results about Cauchy Improper Integral," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 1, no. Issue 2, pp. 08-10, 2022. DOI: https://doi.org/10.54216/GJMSA.010201

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