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Tytuł artykułu

Analytical properties of the two-variables Jacobi matrix polynomials with applications

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived. Furthermore, some relationships and applications are reported.
Wydawca
Rocznik
Strony
178--188
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • Mathematics Department, Faculty of Science, King Khalid University, Abha 61471, Saudi Arabia
  • Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
  • Mathematics Department, Faculty of Science, King Khalid University, Abha 61471, Saudi Arabia
Bibliografia
  • [1] G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
  • [2] E. Rainville, Special Functions, The Macmillan, New York, NY, USA, 1960.
  • [3] D. Kumar and F. Ayant, Application of Jacobi polynomial and multivariable aleph-function in heat conduction in nonhomogeneous moving rectangular parallelepiped, Kragujevac J. Math. 45(2021), no. 3, 439-448.
  • [4] A. Ylmazer, Jacobi polynomials approximation to the one-speed neutron transport equation, Ann. Nucl. Energy 34(2007), 977-991.
  • [5] B. Guo, Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations, J. Math. Anal. Appl. 243(2000), no. 2, 373-408.
  • [6] Y. Prasad and R. Maurya, Application of Jacobi polynomial and multivariable H-function in heat conduction in nonhomogeneous moving rectangular parallelepiped, Bull. Math. Soci. Sci. 24(1980), 393-400.
  • [7] M. Abdalla, Special matrix functions: characteristics, achievements and future directions, Linear Multilinear Algebra 68(2020), no. 1, 1-28.
  • [8] A. Mathai and H. Haubold, An Introduction to Fractional Calculus, NOVA Science Publishers, New York, 2017.
  • [9] L. Rodman, Orthogonal matrix polynomials, in: P. Nevai (ed.), Orthogonal Polynomials: Theory and Practice, NATO ASI Series (Mathematical and Physical Sciences), Springer, Berlin, Germany, 1990, vol. 294, pp. 345-362.
  • [10] H. Fuli, A. Bakhet, M. Hidan, and M. Abdalla, On the extended hypergeometric matrix functions and their applications forthe derivatives of the extended Jacobi matrix polynomial, Math. Probl. Eng. 2020(2020), 4268361.
  • [11] M. Hidan and M. Abdalla, A note on the Appell hypergeometric matrix function F2, Math. Probl. Eng. 2020(2020), 6058987.
  • [12] M. Abdalla, On Hankel transforms of generalized Bessel matrix polynomials, AIMS Mathematics 6(2021), 6122-6139.
  • [13] M. Abdalla, S. Boulaaras, and M. Akel, On Fourier-Bessel matrix transforms and applications, Math. Methods Appl. Sci. (2021), DOI: https://doi.org/10.1002/mma.7489.
  • [14] M. Abdalla, M. Akel, and J. Choi, Certain matrix Riemann-Liouville fractional integrals associated with functions involving generalized Bessel matrix polynomials, Symmetry 13(2021), no. 4, 622, DOI: https://doi.org/10.3390/sym13040622.
  • [15] M. Hidan, M. Akel, S. Boulaaras, and M. Abdalla, On behavior Laplace integral operators with generalized bessel matrix polynomials and related functions, J. Funct. Spaces 2021(2021), 9967855, DOI: https://doi.org/10.1155/2021/9967855.
  • [16] N. J. Higham,Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics (SIAM), USA, 2008.
  • [17] E. Defez, L. Jódar, and A. Law, Jacobi matrix differential equation, polynomial solutions, and their properties, Comput. Math. Appl. 48(2004), no. 5-6, 789-803.
  • [18] B. Çekim, A. Altin, and R. Aktas, Some new results for Jacobi matrix polynomials, Filomat 27(2013), 713-719.
  • [19] M. Hidan, M. Mostefaoui, and M. Abdalla, On the matrix versions of pseudo Jacobi polynomials, J. Sci. Arts 19(2019), no. 3, 629-636.
  • [20] A. Bakhet and F. He, On-2 variables Konhauser matrix polynomials and their fractional integrals, Mathematics 8(2020), no. 2, 232, DOI: https://doi.org/10.3390/math8020232.
  • [21] F. He, A. Bakhet, M. Hidan, and M. Abdalla, Two variables Shivley’s matrix polynomials, Symmetry 11(2019), 151, DOI: http://dx.doi.org/10.3390/sym11020151.
  • [22] S. Khan and N. M. Hassan, 2-variable Laguerre matrix polynomials and Lie-algebraic techniques, J. Phys. A: Math. Theor. 43(2010), 235204, DOI: https://doi.org/10.1088/1751-8113/43/23/235204.
  • [23] S. Khan and N. Raza, 2-variable generalized Hermite matrix polynomials and Lie algebra representation, Rep. Math. Phys. 66(2010), 159-174.
  • [24] G. S. Kahmmash, A study of a two-variables Gegenbauer matrix polynomials and second order matrix partial differential equations, Int. J. Math. Anal. 2(2008), 807-821.
  • [25] L. Kargin and V. Kurt, Chebyshev-type matrix polynomials and integral transforms, Hacet. J. Math. Stat. 44(2015), 341-350.
  • [26] R. Khan, N. Kumar, and R. Qamar, Two variables generalization of Jacobi polynomials, Glob. J. Pure Appl. Math. 13(2017), 1387-1399.
  • [27] J. C. Cortȩs, L. Jǫdar, F. J. Sols, and R. Ku Carrillo, Infinite matrix products and the representation of the gamma matrix function, Abstr. Appl. Anal. 2015(2015), 564287, DOI: https://doi.org/10.1155/2015/564287.
  • [28] F. Taşdelen, B. Çekim, and R. Aktaş, On a multivariable extension of Jacobi matrix polynomials, Comput. Math. Appl. 61(2011), 2412-2423.
  • [29] M. T. Mohammed and A. Shehata, A study of Appell’s matrix functions of two complex variables and some properties, Adv. Appl. Math. Sci. 9(2011), no. 1, 23-33.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9287c79f-1261-4690-be88-bbea703cdfac
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