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Title

The Integrals on Spherical Regions in ℜn

  Murat Ozcek 1 *

1  Gaziantep University, Gaziantep, Turkey
    (muratozcek.12@gmail.com)


Doi   :   https://doi.org/10.54216/GJMSA.070204

Received: March 25, 2023 Revised: June 23, 2023 Accepted: August 22, 2023

Abstract :

This paper is dedicated to find the values of the integrals in the spherical region of  depending on the generative Kernel method by finding the integral formula that we use in the orthogonal and regular operations to find Ortho-normal polynomials on the sphere with radius r. Also, we illustrate many examples to clarify the validity of our work.

Keywords :

Generative kernel; spherical region; Euclidean space; integral formula

References :

[1]. G. PETROVA. 2004- Cubature Formulae For Spheres, Simplices And Balls. Taxas A&M University., Journal Of Computational And Applied Mathematics. 162,483-496.

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[4] H.M. Moller, 1973-POLYNOMIALS AND CUBATURE FORMULAE, Ph.D. Thesis, Univ. Dortmund.

[5]. I.P. MYSOVSKIKH. 1969-Cubature Formulae And Orthogonal Polynomials. Zh. Vychisl. Mat. I Mat. Fiz., 9(2): 419- 425.

[6]. I.P. MYSOVSKIKH. 1969-The Construction Of Interpolation Cubature Formulae With The Least Number Of Nodes. Tr. II. Respubl. Konf. Mat. Belorussii, Pages 42-48. 1969. (Russian), ZB 194. 18703.

[7]. I.P. MYSOVSKIKH. 1981- Interpolation Cubature Formulas. Moskva: “Nauka”. 336p., Moscow-Leningrad.

[8]. I.P. MYSOVSKIKH. 1985- Cubature Formulas In The Case Of Central Symmetry. Netody Vychisl., 14:35. (Russian), MR 90f:65035, ZB 754.41028.

[9].I.P. MYSOVSKIKH. 1995-Representation Of The Reproducing Kernels Of A Ball. Metody Vychisl., 17:145-152.

[10]. I.P. MYSOVSKIKH. 1996-A representation Of The Reproducing Kernels Of A Shpere. Zh. Vychisl. Mat. I mat. Fiz., 36(3):28-34, (Russian), Comput. Maths math. Phys. 36(3), 303- 308(English).

[11]. KH. A. ABBAS and I.P. MYSOVSKIKH. 1991-On The Method Of Reproducing Kernel For Constructing Cubature Formulae. Vestnik Leninger. Univ., Ser. I, 22(4): 3-11. (Russian).

[12]. R. COOLS, I.P. MYSOVSKIKH, and H.J. Schmid. 2001- Cubature Formulae And Orthogonal Polynomials.J. Comput. Apply. Math., 127:121-152.


Cite this Article as :
Style #
MLA Murat Ozcek. "The Integrals on Spherical Regions in ℜn." Galoitica: Journal of Mathematical Structures and Applications, Vol. 7, No. 2, 2023 ,PP. 34-46 (Doi   :  https://doi.org/10.54216/GJMSA.070204)
APA Murat Ozcek. (2023). The Integrals on Spherical Regions in ℜn. Journal of Galoitica: Journal of Mathematical Structures and Applications, 7 ( 2 ), 34-46 (Doi   :  https://doi.org/10.54216/GJMSA.070204)
Chicago Murat Ozcek. "The Integrals on Spherical Regions in ℜn." Journal of Galoitica: Journal of Mathematical Structures and Applications, 7 no. 2 (2023): 34-46 (Doi   :  https://doi.org/10.54216/GJMSA.070204)
Harvard Murat Ozcek. (2023). The Integrals on Spherical Regions in ℜn. Journal of Galoitica: Journal of Mathematical Structures and Applications, 7 ( 2 ), 34-46 (Doi   :  https://doi.org/10.54216/GJMSA.070204)
Vancouver Murat Ozcek. The Integrals on Spherical Regions in ℜn. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 7 ( 2 ): 34-46 (Doi   :  https://doi.org/10.54216/GJMSA.070204)
IEEE Murat Ozcek, The Integrals on Spherical Regions in ℜn, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 7 , No. 2 , (2023) : 34-46 (Doi   :  https://doi.org/10.54216/GJMSA.070204)