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Journals / Mathematical and Computational Applications / 2013 / Cilt: 18 - Sayı: 3

SOME RELATIONS ON HERMITE MATRIX POLYNOMIALS

Levent KARGİN
Veli KURT
Pages
323–329
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also obtain a new generating function for Hermite matrix polynomials and using this function, we prove some new results and relations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study we give addition theorem, multiplication theorem and summation formula for Hermite matrix polynomials.
📊
Key Findings & Data:We write Hermite matrix polynomials as hypergeometric matrix functions.
💡
Conclusion & Impact:We also obtain a new generating function for Hermite matrix polynomials and using this function, we prove some new results and relations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study we give addition theorem, multiplication theorem and summation formula for Hermite matrix polynomials. We write Hermite matrix polynomials as hypergeometric matrix functions. We also obtain a new generating function for Hermite matrix polynomials and using this function, we prove some new results and relations.

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Cite This Article

KARGİN, L., KURT, V. (2013). SOME RELATIONS ON HERMITE MATRIX POLYNOMIALS. Mathematical and Computational Applications, Cilt: 18 - Sayı: 3, 323–329. https://ajindex.com/articles/279799

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References (17)

  1. F. Brafman, Generating functions of Jacobi and related polynomials, Proceedings of the American Mathematical Society 2 (6), 942-949, 1951
  2. F. Brafman, Some generating functions for Laguerre and Hermite polynomials, Canadian Journal of Mathematics 9, 180-187, 1957
  3. E. Defez and L. Jodar, Some applications of the Hermite matrix polynomials series expansions, Journal of Computational Applied Mathematics 99, 105-117, 1998
  4. E. Defez and L. Jodar, Chebyshev matrix polynomials and second order matrix differential equations, Utilitas Mathematica 62, 107-123, 2002.5. E. Defez and L. Jodar, Jacobi Matrix Differential Equation, Polynomial Solutions, and their Properties, Computers and Mathematics with Applications 48, 789-803, 2004
  5. N. Dunford and J. Schwartz, Linear Operators, Vol. I, Interscience, New York, 1963
  6. L. Jodar, R. Company and E. Ponsoda, Orthogonal matrix polynomials and systems of second order differential equations, Differential Equations and Dynamical Systems 3 (3), 269-288, 1995
  7. L. Jodar, R. Company and E. Navarro: Laguerre matrix polynomials and systems of second order differential equations, Applied Numerical Mathematics 15, 53-63, 1994
  8. L. Jodar and R. Company: Hermite matrix polynomials and second order matrix differential equations, Approximation Theory and its Applications 12 (2), 20-30, 1996
  9. L. Jodar, J. C. Cortes, Some properties of gamma and beta functions, Applied Mathematics Letters 11(1), 89-93, 1998
  10. L. Jodar and J. C. Cortes, On the hypergeometric matrix function, Journal of Computational and Applied Mathematics 99, 205-217, 1998
  11. L. Jodar and J. C. Cortes, Closed form solution of the hypergeometric matrix differential equation, Mathematical and Computer Modelling 32, 1017-1028, 2000
  12. L. Jodar and J. Sastre, On the Laguerre matrix polynomials, Utilitas Mathematica 53, 37-48,.1998
  13. L. Jodar, E. Defez, Some new matrix formulas related to hermite matrix polynomials theory, Proceedings of the Internatinal Workshop on Orthogonal Polynomials in Mathematical Physics, Leganes, 1996
  14. L. Jodar and E. Defez, On Hermite matrix polynomials and Hermite matrix function, Approximation Theory and its Applications 14 (1), 36-48, 1998
  15. P. Lancaster, Theory of Matrices, Academic Press, New York, 1969
  16. M. S. Metwally, M. T. Mohamed and A. Shehata, On Hermite-Hermite matrix polynomials, Mathematica Bohemica 133 (4), 421-434, 2008
  17. M. S. Metwally, M. T. Mohamed and A. Shehata, Generalizations of