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On generalized Laguerre matrix polynomials

Acta Universitatis Sapientiae, Mathematica
Volume 10 (2018): Issue 1 (August 2018)
By:
Open Access
|Sep 2018

References

  1. [1] R. S. Batahan, A new extension of Hermite matrix polynomials and its applications, Linear Algebra Appl., 419 (2006), 82–92.10.1016/j.laa.2006.04.006
    Search in Google ScholarBack to article
  2. [2] R. S. Batahan, Generalized Gegenbauer matrix polynomials, series expansion and some properties, In: Linear Algebra Research Advances, Editor G. D. Ling, Nova Science Publishers, (2007), 291–305.
    Search in Google ScholarBack to article
  3. [3] E. Defez and L. Jódar, Some applications of the Hermite matrix polynomials series expansions, J. Comp. Appl. Math., 99 (1998), 105–117.10.1016/S0377-0427(98)00149-6
    Search in Google ScholarBack to article
  4. [4] E. Defez and L. Jódar, Chebyshev matrix polynomials and second order matrix differential equations, Util. Math., 61 (2002), 107–123.
    Search in Google ScholarBack to article
  5. [5] N. Dunford and J. Schwartz, Linear Operators, Vol. I, Interscience, New York, (1957).
    Search in Google ScholarBack to article
  6. [6] E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, New York, (1969).
    Search in Google ScholarBack to article
  7. [7] L. Jódar and R. Company, Hermite matrix polynomials and second order matrix differential equations, J. Approx. Theory Appl., 12 (2) (1996), 20–30.10.1007/BF02836202
    Search in Google ScholarBack to article
  8. [8] L. Jódar, R. Company and E. Navarro, Laguerre matrix polynomials and system of second-order differential equations, Appl. Num. Math., 15 (1994), 53–63.10.1016/0168-9274(94)00012-3
    Search in Google ScholarBack to article
  9. [9] L. Jódar and J. C. Cortés, Some properties of gamma and beta matrix function, Appl. Math. Lett., 11 (1) (1998), 89–93.10.1016/S0893-9659(97)00139-0
    Search in Google ScholarBack to article
  10. [10] L. Jódar and J. C. Cortés, On the hypergeometric matrix function, J. Comp. Appl. Math., 99 (1998), 205–217.10.1016/S0377-0427(98)00158-7
    Search in Google ScholarBack to article
  11. [11] L. Jódar and E. Defez, On Hermite matrix polynomials and Hermite matrix function, J. Approx. Theory Appl., 14 (1) (1998), 36–48.10.1007/BF02836885
    Search in Google ScholarBack to article
  12. [12] L. Jódar and E. Defez, A Connection between Laguerre’s and Hermite’s matrix polynomials, Appl. Math. Lett. 11 (1) (1998), 13–17.10.1016/S0893-9659(97)00125-0
    Search in Google ScholarBack to article
  13. [13] L. Jódar, E. Defez and E. Ponsoda, Orthogonal matrix polynomials with respect to linear matrix moment functionals: Theory and applications, J. Approx. Theory Appl., 12 (1) (1996), 96–115.10.1007/BF02836898
    Search in Google ScholarBack to article
  14. [14] L. Jódar and J. Sastre, The growth of Laguerre matrix polynomials on bounded intervals, Appl. Math. Lett., 13 (8) (2000), 21–26.10.1016/S0893-9659(00)00090-2
    Search in Google ScholarBack to article
  15. [15] E. D. Rainville, Special Functions, The Macmillan Company, New York, (1960).
    Search in Google ScholarBack to article
  16. [16] J. Sastre and E. Defez, On the asymptotics of Laguerre matrix polynomial for large x and n, Appl. Math. Lett., 19 (2006), 721–727.10.1016/j.aml.2005.10.003
    Search in Google ScholarBack to article
  17. [17] J. Sastre, E. Defez and L. Jódar, Laguerre matrix polynomial series expansion: Theory and computer applications, Math. Comput. Modelling, 44 (2006), 1025–1043.10.1016/j.mcm.2006.03.006
    Search in Google ScholarBack to article
  18. [18] J. Sastre, E. Defez and L. Jódar, Application of Laguerre matrix polynomials to the numerical inversion of Laplace transforms of matrix functions, Appl. Math. Lett., 24 (9) (2011), 1527–1532.10.1016/j.aml.2011.03.039
    Search in Google ScholarBack to article
  19. [19] K. A. M. Sayyed, M. S. Metwally and R. S. Batahan. On Gegeralized Hermite matrix polynomials, Electron. J. Linear Algebra, 10 (2003), 272–279.10.13001/1081-3810.1113
    Search in Google ScholarBack to article
  20. [20] K. A. M. Sayyed, M. S. Metwally and R. S. Batahan. Gegenbauer matrix polynomials and second order matrix differential equations, Divulg. Mat., 12 (2) (2004), 101–115.
    Search in Google ScholarBack to article
  21. [21] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane, and Toronto, (1984).
    Search in Google ScholarBack to article
  22. [22] Z. Zhu and Z. Li. A note on Sobolev orthogonality for Laguerre matrix polynomials, Analysis in Theory and Applications, 23 (1) (2007), 26–34.10.1007/s10496-001-0026-z
    Search in Google ScholarBack to article
DOI: https://doi.org/10.2478/ausm-2018-0003 | Journal eISSN: 2066-7752
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Language: English
Page range: 32 - 45
Submitted on: Jan 5, 2015
Published on: Sep 10, 2018
Published by: Sapientia Hungarian University of Transylvania
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year
Keywords:
Laguerre matrix polynomials,
three terms recurrence relation,
generalized hypergeometric matrix function and Gamma matrix function
Related subjects:
Mathematics,
General mathematics

© 2018 Raed S. Batahan, A. A. Bathanya, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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