On Hermite-Hermite matrix polynomials

M. S. Metwally; M. T. Mohamed; A. Shehata

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 4, page 421-434
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Metwally, M. S., Mohamed, M. T., and Shehata, A.. "On Hermite-Hermite matrix polynomials." Mathematica Bohemica 133.4 (2008): 421-434. <http://eudml.org/doc/250535>.

@article{Metwally2008,
abstract = {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.},
author = {Metwally, M. S., Mohamed, M. T., Shehata, A.},
journal = {Mathematica Bohemica},
keywords = {matrix functions; Hermite matrix polynomials; recurrence relation; Hermite matrix differential equation; Rodrigues's formula; Hermite-Hermite matrix polynomials; recurrence relation; Hermite matrix differential equation; Rodrigues's formula},
language = {eng},
number = {4},
pages = {421-434},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Hermite-Hermite matrix polynomials},
url = {http://eudml.org/doc/250535},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Metwally, M. S.
AU - Mohamed, M. T.
AU - Shehata, A.
TI - On Hermite-Hermite matrix polynomials
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 4
SP - 421
EP - 434
AB - 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.
LA - eng
KW - matrix functions; Hermite matrix polynomials; recurrence relation; Hermite matrix differential equation; Rodrigues's formula; Hermite-Hermite matrix polynomials; recurrence relation; Hermite matrix differential equation; Rodrigues's formula
UR - http://eudml.org/doc/250535
ER -

References

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  2. Defez, E., Jódar, L., 10.1016/S0377-0427(98)00149-6, J. Comput. Appl. Math. 99 (1998), 105-117. (1998) MR1662687DOI10.1016/S0377-0427(98)00149-6
  3. Defez, E., Hervás, A., Jódar, L., Law, A., 10.1016/j.mcm.2003.11.004, Math. Computer Modelling 40 (2004), 117-125. (2004) Zbl1061.33007MR2091530DOI10.1016/j.mcm.2003.11.004
  4. Jódar, L., Company, R., Hermite matrix polynomials and second order matrix differential equations, J. Approx. Theory Appl. 12 (1996), 20-30. (1996) MR1465570
  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. MR1466771
  6. Jódar, L., Defez, E., 10.1016/S0893-9659(97)00125-0, Appl. Math. Lett. 11 (1998), 13-17. (1998) Zbl1074.33011MR1490373DOI10.1016/S0893-9659(97)00125-0
  7. Jódar, L., Defez, E., On Hermite matrix polynomials and Hermite matrix functions, J. Approx. Theory Appl. 14 (1998), 36-48. (1998) MR1651470
  8. Lebedev, N. N., Special Functions and Their Applications, Dover, New York (1972). (1972) Zbl0271.33001MR0350075
  9. Rainville, E. D., Special Functions, Macmillan, New York (1962). (1962) MR0107725
  10. Sayyed, K. A. M., Metwally, M. S., Batahan, R. S., On generalized Hermite matrix polynomials, Electron. J. Linear Algebra 10 (2003), 272-279. (2003) Zbl1038.33005MR2025009
  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. (2004) Zbl1102.33010MR2123993
  12. Srivastava, H. M., Manocha, H. L., A Treatise on Generating Functions, Ellis Horwood, New York (1984). (1984) Zbl0535.33001MR0750112

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