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Abstrakty
In this paper, we introduce a new generalization of the Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems. An explicit representation and an expansion of the matrix exponential in a series of these matrix polynomials is obtained. Properties of Hermite matrix polynomials such as the recurrence formula permit an efficient computations of matrix functions are established. A new expansions of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.
Wydawca
Czasopismo
Rocznik
Tom
Strony
687--701
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
autor
autor
- Department of Mathematics Faculty of Science Assiut University Assiut 71516, Egypt, Kamel702007@yahoo.com
Bibliografia
- [1] P. Appell, J. Kampé de Feriet, Functions Hypergéométrique et Hypersphériques Polynômes d'Hermite, Gauthier-Villars, Paris, 1926.
- [2] R. S. Batahan, A new extension of Hermite matrix polynomials and its applications, Linear Algebra Appl. 419 (2006), 82-92.
- [3] J. L. Burchnall, A note on the polynomials of Hermite, Quart. J. Math. Oxford Ser. (2) 12 (1941), 9-11.
- [4] E. Defez, L. Jódar, Some applications of Hermite matrix polynomials series expansions, J. Comput. Appl. Math. 99 (1998), 105-117.
- [5] E. Defez, A. Hervás, L. Jódar, A. Law, Bounding Hermite matrix polynomials, Math. Computer Modell. 40 (2004), 117-125.
- [6] N. Dunford, J. Schwartz, Linear Operators, part I, Interscience, New York, 1956.
- [7] L. Jódar, R. Company, Hermite matrix polynomials and second order matrix differential equations, J. Approx. Theory Appl. 12 (1996), 20-30.
- [8] L. Jódar, E. Defez, Some new matrix formulas related to Hermite matrix polynomials theory, Proceedings Int. Workshop Orth. Poly. Math. Phys., Leganés. (1996), 93-101.
- [9] L. Jódar, E. Defez, On Hermite matrix polynomials and Hermite matrix functions, J. Approx. Theory Appl. 14 (1998), 36-48.
- [10] L. Jódar, E. Defez, A connection between Lagurre’s and Hermite’s matrix polynomials, Appl. Math. Lett. 11 (1998), 13-17.
- [11] L. Jódar, J. Pérez, R. J. Villanueva, Analytic and numerical solution of coupled implicit semi-infinite diffusion problems, Comput. Math. Appl. 41 (2001), 447-459.
- [12] L. Jódar, J. Pérez, R. J. Villanueva, Explicit solution of time dependent diffusion problems in a semi-infinite medium, Comput. Math. Appl. 43 (2002), 157-167.
- [13] M. Lahiri, An associated generatized Hermite polynomials, Proc. Amer. Math. Soc. 27 (1971), 117-121.
- [14] N. N. Lebedev, Special Functions and their Applications, Dover, New York, 1972.
- [15] M. S. Metwally, M. T. Mohamed, A. Shehata, On Hermite-Hermite matrix polynomials, Math. Bohem. 133 (2008), 421-434.
- [16] I. Najfeld, T. F. Havel, Derivaties of the matrix exponential and thier computation, Adv. Appl. Math. 16 (1995), 321-375.
- [17] M. M. Nieto, D. Rodney Truax, Arbitrary-order Hermite generating functions for obtaining arbitrary-order coherent and squeezed states, Phys. Lett. A 208 (1995), 8-16.
- [18] E. D. Rainville, Special Functions, Macmillan, New York, 1962.
- [19] K. A. M. Sayyed, M. S. Metwally, R. S. Batahan, On generalized Hermite matrix polynomials, Electron. J. Linear Algebra 10 (2003), 272-279.
- [20] K. A. M. Sayyed, M. S. Metwally, R. S. Batahan, Gegenbauer matrix polynomials and second order matrix differential equations, Divulg. Mat. 12 (2004), 101-115.
- [21] H. M. Srivastava, H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood, New York, 1984.
- [22] J. Uspensky, On the development of arbitrary functions in series of Hermite’s and LaguerreŠs polynomials, Annuls of Maths. 28 (1927), 593-619.
- [23] D. V. Widder, The Heat Equation, Academic Press, New York, 1975.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0027-0003