Some relations on Humbert matrix polynomials

Ayman Shehata

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 4, page 407-429
  • ISSN: 0862-7959

Abstract

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The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.

How to cite

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Shehata, Ayman. "Some relations on Humbert matrix polynomials." Mathematica Bohemica 141.4 (2016): 407-429. <http://eudml.org/doc/287552>.

@article{Shehata2016,
abstract = {The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.},
author = {Shehata, Ayman},
journal = {Mathematica Bohemica},
keywords = {hypergeometric matrix function; Humbert matrix polynomials; matrix functional calculus; generating matrix function; matrix differential equation},
language = {eng},
number = {4},
pages = {407-429},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some relations on Humbert matrix polynomials},
url = {http://eudml.org/doc/287552},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Shehata, Ayman
TI - Some relations on Humbert matrix polynomials
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 4
SP - 407
EP - 429
AB - The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.
LA - eng
KW - hypergeometric matrix function; Humbert matrix polynomials; matrix functional calculus; generating matrix function; matrix differential equation
UR - http://eudml.org/doc/287552
ER -

References

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