On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk

Rashel Abu

doi:https://doi.org/10.54216/PMTCS.020202

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Volume 2 • Issue 2 • PP: 23-29 • 2023

On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk

Rashel Abu Hakmeh ^1*

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¹Faculty of Science, Mutah University, Jordan

* Corresponding Author.

DOI https://doi.org/10.54216/PMTCS.020202

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Received: January 20, 2023 Revised: April 15, 2023 Accepted: September 19, 2023

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Abstract

In this paper, we find the formula of Cauchy – Pompeiu's integral in the octal of unit disk of the complex plain, by using the reflection method to determine the Integral's Cauchy – Pompeiu's operator. Also, we give many related examples about the novel formula.

Keywords

Cauchy &ndash Pompeiu's integral reflection Cauchy &ndash Pompeiu's operator

References

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[4] H. Begehr, S.Burgumbayeva, B.Shupeyeva, Harmonic Green Functions for a Plane Domain With two Touching Circles as Boundary, Advanced Mathematical Models & Applications, vol.3, no.1, pp. 18–29, (2018).

[5] Y. Wang, Boundary value problems for complex partial differential equations in fanshaped domains, Ph.D. thesis, FU Berlin, (2011), ttp://www.diss.fuberlin.de/diss/receive.FUDISS-thesis-000000021359.

[6] B.Shupeyeva, Some Basic Boundary Value Problems for Complex Partial Differential Equations in Quarter Ring and Half Hexagon, Ph.D. thesis, FU Berlin,(2013).

[7] T.Vaitsiakhovich, Boundary Value Problems for Complex Partial Differential Equations in a ring domain, PhD thesis, FU Berlin, 2008; www.diss.fu-berlin.de/diss/receive/FUDISS thesis 000000003859.

[8] H.Begehr, , T.Vaitekhovich, Schwarz problem in lens and lune. Complex Var. Ell. Eq., 59(1), 76–84 (2014).

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Hakmeh, Rashel Abu. "On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk." Pure Mathematics for Theoretical Computer Science, vol. Volume 2, no. Issue 2, 2023, pp. 23-29. DOI: https://doi.org/10.54216/PMTCS.020202

Hakmeh, R. (2023). On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk. Pure Mathematics for Theoretical Computer Science, Volume 2(Issue 2), 23-29. DOI: https://doi.org/10.54216/PMTCS.020202

Hakmeh, Rashel Abu. "On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk." Pure Mathematics for Theoretical Computer Science Volume 2, no. Issue 2 (2023): 23-29. DOI: https://doi.org/10.54216/PMTCS.020202

Hakmeh, R. (2023) 'On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk', Pure Mathematics for Theoretical Computer Science, Volume 2(Issue 2), pp. 23-29. DOI: https://doi.org/10.54216/PMTCS.020202

Hakmeh R. On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk. Pure Mathematics for Theoretical Computer Science. 2023;Volume 2(Issue 2):23-29. DOI: https://doi.org/10.54216/PMTCS.020202

R. Hakmeh, "On Finding Cauchy – Pompeiu's Formula in The Octal Unit Disk," Pure Mathematics for Theoretical Computer Science, vol. Volume 2, no. Issue 2, pp. 23-29, 2023. DOI: https://doi.org/10.54216/PMTCS.020202

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