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ISSN : 1226-0657

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Vol.21 No.3
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ON MATRIX POLYNOMIALS ASSOCIATED WITH HUMBERT POLYNOMIALS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2014, v.21 no.3, pp.207-218
https://doi.org/10.7468/jksmeb.2014.21.3.207
Pathan, M.A.
Bin-Saad, Maged G.
Al-Sarahi, Fadhl
Pathan,, M. , Bin-Saad,, M. G. , & Al-Sarahi,, F. (2014). ON MATRIX POLYNOMIALS ASSOCIATED WITH HUMBERT POLYNOMIALS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 21(3), 207-218, https://doi.org/10.7468/jksmeb.2014.21.3.207
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Abstract

The principal object of this paper is to study a class of matrix polynomials associated with Humbert polynomials. These polynomials generalize the well known class of Gegenbauer, Legendre, Pincherl, Horadam, Horadam-Pethe and Kinney polynomials. We shall give some basic relations involving the Humbert matrix polynomials and then take up several generating functions, hypergeometric representations and expansions in series of matrix polynomials.

keywords
hypergeometric matrix function, Humbert matrix polynomials, generating matrix function, generating relations, Gegenbauer matrix polynomials

Reference

1.

R. Aktas. (2014). A Note on multivariable Humbert matrix Polynomials. Gazi University journal of science, 27(2), 747-754.

2.

R. Aktas. (2013). A New multivariable extension of Humbert matrix Polynomials (1128-1131). AIP Conference Proceedings.

3.

H.W. Gould. (1965). Inverse series relation and other expansions involving Humbert polynomials. Duke Math. J., 32, 697-711. 10.1215/S0012-7094-65-03275-8.

4.

R. Aktas, B. Cekim & R. Sahin. (2012). The matrix version of the multivariable Humbert matrix Polynomials. Miskolc Mathematical Notes, 13(2), 197-208.

5.

R.S. Batahan. (2006). A New extension of Hermite matrix Polynomials and its applications. LinearAlgebra Appl., 419, 82-92.

6.

G. Dattoli, B. Ermand & P.E. Riccl. (2004). Matrix Evolution equation and special functions. computer and mathematics with Appl., 48, 1611-1617. 10.1016/j.camwa.2004.03.007.

7.

A. Horadam. (1985). Polynomials associated with Gegenbauer Polynomials. Fibonacci Quart., 23, 295-399.

8.

A. Horadan & S. Pethe. (1981). Gegenbauer polynomials revisited. Fibonacci Quart., 19, 393-398.

9.

L. Jodar & E. Defez. (1998). On Some properties of Humbert's polynomials II. Facta Universityis (Nis) ser. Math., 6, 13-17.

10.

G.V. Milovanovic & G.B. Dordevic. (1991). A connection between laguerre"s and Hermite's matrix polynomials. Appl. Math. Lett., 11, 23-30.

11.

M.A. Pathan & M.A. Khan. on Polynomials associated with Humbents polynomials. publications DEL, Intitut Mathematique, Noavelle seris 62.

12.

E.D. Rainville. Special function.

13.

J. Sastre, E. Defez & L. Jodar. (2006). Laguerre matrix polynomials. series expansion: theory and computer applications. Mathematical and computer Modelling, 44, 1025-1043. 10.1016/j.mcm.2006.03.006.

14.

K.A. Sayyed, M.S. Metwally & R.S. Batahn. (2004). Gegenbauer matrix polynomials and second order Matrix Differential Equations. Div., Math., 12, 101-115.

15.

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

16.

N.B. Shrestha. (1977). Polynomial associated with Legendre polynomials. Nepali , Yath. Sci. Rep. Triv., 2(1), 1-7.

17.

S.K. Sinha. (1989). On a polynomial associated with Gegenbauer polynomial. Proc. Not. Acad. Sci. India, 54, 439-455.

18.

H.M. Srivastava & H.L. Manocha. A treatise on Generating functions.

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