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Galoitica: Journal of Mathematical Structures and Applications
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Title

Some Results about Cauchy Improper Integral

  Arwa Hajjari 1 *

1  Cairo University, Cairo, Egypt
    (Hajjarint8843@gmail.com)

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

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

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.

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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

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MLA Arwa Hajjari. "Some Results about Cauchy Improper Integral." Galoitica: Journal of Mathematical Structures and Applications, Vol. 1, No. 2, 2022 ,PP. 08-10 (Doi   :  https://doi.org/10.54216/GJMSA.010201)
APA Arwa Hajjari. (2022). Some Results about Cauchy Improper Integral. Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 2 ), 08-10 (Doi   :  https://doi.org/10.54216/GJMSA.010201)
Chicago Arwa Hajjari. "Some Results about Cauchy Improper Integral." Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 no. 2 (2022): 08-10 (Doi   :  https://doi.org/10.54216/GJMSA.010201)
Harvard Arwa Hajjari. (2022). Some Results about Cauchy Improper Integral. Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 2 ), 08-10 (Doi   :  https://doi.org/10.54216/GJMSA.010201)
Vancouver Arwa Hajjari. Some Results about Cauchy Improper Integral. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2022); 1 ( 2 ): 08-10 (Doi   :  https://doi.org/10.54216/GJMSA.010201)
IEEE Arwa Hajjari, Some Results about Cauchy Improper Integral, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 1 , No. 2 , (2022) : 08-10 (Doi   :  https://doi.org/10.54216/GJMSA.010201)
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