1
Gaziantep University, Gaziantep, Turkey
(muratozcek.12@gmail.com)
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.
[2]. H. M. Moller, 1976- Cubature Formulae mit minimaler Knotenzahl, Numer. Math., 35, pp.185-200.
[3] H. M. Moller, 1979- Lower bounds for the number of nodes in cubature formulae, Numerical Integration, Internat. Ser. Numer. Math. Vol. 45, G. Hammerlin, ed., Birkhauser, Basel.
[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.
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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) |