Some relations satisfied by Hermite-Hermite matrix polynomials

Ayman Shehata; Lalit Mohan Upadhyaya

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 2, page 145-162
  • ISSN: 0862-7959

Abstract

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The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials.

How to cite

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Shehata, Ayman, and Upadhyaya, Lalit Mohan. "Some relations satisfied by Hermite-Hermite matrix polynomials." Mathematica Bohemica 142.2 (2017): 145-162. <http://eudml.org/doc/288105>.

@article{Shehata2017,
abstract = {The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials.},
author = {Shehata, Ayman, Upadhyaya, Lalit Mohan},
journal = {Mathematica Bohemica},
keywords = {Hermite-Hermite polynomials; matrix generating functions; orthogonality property; Rodrigues formula; associated Hermite-Hermite polynomials; generalized Hermite-Hermite matrix polynomials; generalized Hermite matrix polynomials; generating matrix function; matrix recurrence relations; generalized Chebyshev and Legendre matrix polynomials},
language = {eng},
number = {2},
pages = {145-162},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some relations satisfied by Hermite-Hermite matrix polynomials},
url = {http://eudml.org/doc/288105},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Shehata, Ayman
AU - Upadhyaya, Lalit Mohan
TI - Some relations satisfied by Hermite-Hermite matrix polynomials
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 2
SP - 145
EP - 162
AB - The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials.
LA - eng
KW - Hermite-Hermite polynomials; matrix generating functions; orthogonality property; Rodrigues formula; associated Hermite-Hermite polynomials; generalized Hermite-Hermite matrix polynomials; generalized Hermite matrix polynomials; generating matrix function; matrix recurrence relations; generalized Chebyshev and Legendre matrix polynomials
UR - http://eudml.org/doc/288105
ER -

References

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