On Matrix polynomials associated with Hermite polynomials

Authors

  • Maged G. Bin-Saad Math Dept, Special functions
  • M. A. Pathan
  • Fadhl AL-Sarhi

DOI:

https://doi.org/10.5556/j.tkjm.46.2015.1722

Keywords:

Hypergeometric function, Hermite matrix polynomials, gen- erating function, Legendre and Chebyshev matrix polynomials.

Abstract

In this paper, an extension of the Hermite matrix polynomials is introduced. Some relevant matrix functions appear in terms of the two-index and two-variable and p-index and p-variable Hermite matrix polynomials. Furthermore, in order to give qualitative properties of this family of matrix polynomials, the Legendre and Chebyshev matrix polynomials of sveral variables are introduced.

Author Biographies

Maged G. Bin-Saad, Math Dept, Special functions

Department ofMathematics, Aden University, Kohrmakssar P.O.Box 6014, Yemen.

M. A. Pathan

Centre forMathematical and statistical Sciences (CMSS), KFRI, Peechi P.O., Thrissur, Kerala-680653, India.

Fadhl AL-Sarhi

Department ofMathematics, Aden University, Kohrmakssar P.O.Box 6014, Yemen.

References

R. S. Batahan, A new extension of Hermite matrix polynomial and its pplications, LinearAlgebra Appl., 419 (2006), 82--92.

P. J. Davis, Interpolation and Approximation, Vover, Now York, 1975.

L. Jodar, E. Defez and E. Ponsoda, Orthogonal matrix polynomials with respect to liner matrix moment functionals; Theory and Applications, J.Approx. Theory Applications, (12) (1996), 96--115.

L. Jodar and R. Company, Hermite matrix polynomials and second order matrix differential equations, J. Approx. Theory Applications,(12)2(1996), 20--30.

L. Jodar, R. Company and E. Navarro, Laguerre matrix polynomials and system of second order differential equations, Appl. Numer. Math.,15(1994), 53--63.

K. A.M. Sayyed, M. S. Metwally and R. S. Batahan, Gegenbauer matrix polynomials and second order matrix differential equations, Div., Math., (12)2(2004),

--115.

K.A. M. Sayyed, M. S. Metwally and R.S. Batahan, On generalized Hermite matrix polynomials, Electronic Journal of linear Algebra, 10(2003),272--279.

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted press, John Wiley and Sons., New York, 1984.

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Published

2015-06-30

How to Cite

Bin-Saad, M. G., Pathan, M. A., & AL-Sarhi, F. (2015). On Matrix polynomials associated with Hermite polynomials. Tamkang Journal of Mathematics, 46(2), 167-177. https://doi.org/10.5556/j.tkjm.46.2015.1722

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