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OPERATIONAL IDENTITIES FOR HERMITE-PSEUDO LAGUERRE TYPE MATRIX POLYNOMIALS AND THEIR APPLICATIONS

  • Bin-Saad, Maged G. (Department of Mathematics, Aden University) ;
  • Pathan, M.A. (Centre for Mathematical and statistical Sciences (CMSS), KFRI)
  • Received : 2017.10.15
  • Accepted : 2019.01.28
  • Published : 2019.03.25

Abstract

In this work, it is shown that the combination of operational techniques and the use of the principle of quasi-monomiality can be a very useful tool for a more general insight into the theory of matrix polynomials and for their extension. We explore the formal properties of the operational rules to derive a number of properties of certain class of matrix polynomials and discuss the operational links with various known matrix polynomials.

Keywords

References

  1. R. S. Batahan, A new extension of Hermite matrix polynomial and its applications, Linear Algebra Appl., 419 (2006), 82-92. https://doi.org/10.1016/j.laa.2006.04.006
  2. Maged G. Bin-Saad and Antar Ali Al-Sayaad, Study of two variable matrix Laguerre via symbolic operational images, Asian J. of Math. and Computer Research,2(1)(2015), 42-50.
  3. Maged G. Bin-Saad, A new class of Hermite-Konhauser polynomials together with Differential Equations, Kyungpook Math. J., 50 (2010), 237-253. https://doi.org/10.5666/KMJ.2010.50.2.237
  4. G. Dattoli , Pseudo Laguerre and pseudo Hermite polynomials, Rend. Mat. Acc. Lincei., s. 9, v. 12(2001), 75-84.
  5. G. Dattoli , Hermite-Bessel and Laguerre-Bessel functions: A by product of the monomiality principle, Advanced special functions and applications, Proc. Melfi Sch. Adv. Top. Math. Phys. 1(2000), 147-164.
  6. G. Dattoli, Mancho, A.M., Quattromini and A., Torre, A., Generalized polynomials, operational identities and their applications, Radiation Physics and Chemistry, 57(2001), 99-108.
  7. E. Defez, L. Jodar, Some applications of the Hermite matrix polynomials series expansions, Journal of Computational Applied Mathematics, 99(1998) 105-117. https://doi.org/10.1016/S0377-0427(98)00149-6
  8. E. Defez and L. Jodar, Chebyshev matrix polynomials and second order matrix differential equations, Utilitas Mathematica, 62(2002), 107-123.
  9. E. Defez and L. Jodar, Jacobi Matrix Differential Equation, Polynomial Solutions, and their Properties, Computers and Mathematics with Applications, 48(2004), 789-803. https://doi.org/10.1016/j.camwa.2004.01.011
  10. A.J. Duran, Markov's Theorem for orthogonal matrix polynomials, Can. J. Math. 48 (1996), 1095-1180. https://doi.org/10.4153/CJM-1996-062-4
  11. A.J. Duran and W. Van Assche, Orthogonal matrix polynomials and higher order recurrence relations, Linear Algebra and its Applications, 219 (1995), 261-280. https://doi.org/10.1016/0024-3795(93)00218-O
  12. L. Jodar, R. Company and E. Navarro, Laguerre matrix polynomials and system of second order differential equations, Appl. Num. Math., 15 (1994), 53-63. https://doi.org/10.1016/0168-9274(94)00012-3
  13. L. Jodar, R. Company and E. Navarro, Laguerre matrix polynomials and systems of second order differential equations, Applied Numerical Mathematics, 15(1994), 53-63. https://doi.org/10.1016/0168-9274(94)00012-3
  14. L. Jodar, R. Company and E. Ponsoda, Orthogonal matrix polynomials and systems of second order differential equations, Differential Equations and Dynamical Systems, 3 (3)(1995), 269-288.
  15. L. Jodar and R. Company, Hermite matrix polynomials and second order matrix differential equations, Approximation Theory and its Applications,12 (2)(1996), 20-30.
  16. L. Jodar and J. Sastre, On the Laguerre matrix polynomials, Utilitas Mathematica,53(1998), 37-48.
  17. L. Jodar and E. Defez, Some new matrix formulas related to hermite matrix polynomials theory, Proceedings of the International Workshop on Orthogonal Polynomials in Mathematical Physics, Leganes,(1996).
  18. L. Jodar and E. Defez, On Hermite matrix polynomials and Hermite matrix function, Approximation Theory and its Applications, 14 (1)(1998), 36-48.
  19. M. S. Metwally, M. T. Mohamed and A. Shehata, On pseudo Hermite matrix polynomials of two variables, Banach Journal of Mathematical Analysis, 4(2)(2010),169-178. https://doi.org/10.15352/bjma/1297117251
  20. K.S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, J. Wiley and Sons, New York, 1993.
  21. K. A. M. Sayyed, M. S. Metwally and R.S. Batahan, Gegenbauer matrix polynomials and second order matrix differential equations, Divulgaciones Matematicas,12(2)(2004), 101-115.
  22. M. A. Pathan, Maged G. Bin-Saad and Fadhl Al-Sarhi , On matrix polynomials associated with Hermite matrix polynomials, Tamkang J. of Math.,46(2)(2015),167-177. https://doi.org/10.5556/j.tkjm.46.2015.1722
  23. A. Sinap and W. Van Assche, Orthogonal matrix polynomials and applications, J. Comp. Appl. Math.,66 (1996), 27-52. https://doi.org/10.1016/0377-0427(95)00193-X
  24. J.F. Steffensen, The poweriod, an extension of the mathematical notion of power, Acta Math.,73 (1941), 333-366. https://doi.org/10.1007/BF02392231
  25. S. Varma, B. Cekim and FT. Yesildal, On Konhauser matrix polynomials, Ars Combin., 100 (2011), 193-204.