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matrix functions; Hermite matrix polynomials; recurrence relation; Hermite matrix differential equation; Rodrigues's formula
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite matrix polynomials is proposed.
[1] Batahan, R. S.: A new extension of Hermite matrix polynomials and its applications. Linear Algebra Appl. 419 (2006), 82-92. MR 2263112 | Zbl 1106.15016
[2] Defez, E., Jódar, L.: Some applications of Hermite matrix polynomials series expansions. J. Comput. Appl. Math. 99 (1998), 105-117. DOI 10.1016/S0377-0427(98)00149-6 | MR 1662687
[3] Defez, E., Hervás, A., Jódar, L., Law, A.: Bounding Hermite matrix polynomials. Math. Computer Modelling 40 (2004), 117-125. DOI 10.1016/j.mcm.2003.11.004 | MR 2091530 | Zbl 1061.33007
[4] Jódar, L., Company, R.: Hermite matrix polynomials and second order matrix differential equations. J. Approx. Theory Appl. 12 (1996), 20-30. MR 1465570
[5] Jódar, L., Defez, E.: Some new matrix formulas related to Hermite matrix polynomials theory. Proceedings International Workshop on Orthogonal Polynomials in Mathematical Physics, Leganés, 1996 M. Alfaro Universidad Carlos III. de Madrid, Servicio de Publicaciones, 1997 93-101. MR 1466771
[6] Jódar, L., Defez, E.: A connection between Laguerre's and Hermite's matrix polynomials. Appl. Math. Lett. 11 (1998), 13-17. DOI 10.1016/S0893-9659(97)00125-0 | MR 1490373 | Zbl 1074.33011
[7] Jódar, L., Defez, E.: On Hermite matrix polynomials and Hermite matrix functions. J. Approx. Theory Appl. 14 (1998), 36-48. MR 1651470
[8] Lebedev, N. N.: Special Functions and Their Applications. Dover, New York (1972). MR 0350075 | Zbl 0271.33001
[9] Rainville, E. D.: Special Functions. Macmillan, New York (1962). MR 0107725
[10] Sayyed, K. A. M., Metwally, M. S., Batahan, R. S.: On generalized Hermite matrix polynomials. Electron. J. Linear Algebra 10 (2003), 272-279. MR 2025009 | Zbl 1038.33005
[11] Sayyed, K. A. M., Metwally, M. S., Batahan, R. S.: Gegenbauer matrix polynomials and second order matrix differential equations. Divulg. Mat. 12 (2004), 101-115. MR 2123993 | Zbl 1102.33010
[12] Srivastava, H. M., Manocha, H. L.: A Treatise on Generating Functions. Ellis Horwood, New York (1984). MR 0750112 | Zbl 0535.33001
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