Galoitica: Journal of Mathematical Structures and Applications

Journal DOI

https://doi.org/10.54216/GJSMA

Submit Your Paper

2834-5568ISSN (Online)

Volume 7 , Issue 2 , PP: 34-46, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

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.

    [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.

    Cite This Article As :
    Ozcek, Murat. The Integrals on Spherical Regions in ℜn. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2023, pp. 34-46. DOI: https://doi.org/10.54216/GJMSA.070204
    Ozcek, M. (2023). The Integrals on Spherical Regions in ℜn. Galoitica: Journal of Mathematical Structures and Applications, (), 34-46. DOI: https://doi.org/10.54216/GJMSA.070204
    Ozcek, Murat. The Integrals on Spherical Regions in ℜn. Galoitica: Journal of Mathematical Structures and Applications , no. (2023): 34-46. DOI: https://doi.org/10.54216/GJMSA.070204
    Ozcek, M. (2023) . The Integrals on Spherical Regions in ℜn. Galoitica: Journal of Mathematical Structures and Applications , () , 34-46 . DOI: https://doi.org/10.54216/GJMSA.070204
    Ozcek M. [2023]. The Integrals on Spherical Regions in ℜn. Galoitica: Journal of Mathematical Structures and Applications. (): 34-46. DOI: https://doi.org/10.54216/GJMSA.070204
    Ozcek, M. "The Integrals on Spherical Regions in ℜn," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 34-46, 2023. DOI: https://doi.org/10.54216/GJMSA.070204