Some relations on Humbert matrix polynomials

Ayman Shehata

Mathematica Bohemica (2016)

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

Abstract

top
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

top

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

top
  1. Aktaş, R., 10.1063/1.4825706, AIP Publishing LLC Rhodes, Greece AIP Conference Proceedings 1558: Proc. Int. Conf. on Numerical Analysis and Applied Mathematics (2013), 1128-1131 T. Simos et al. 10.1063/1.4825706. (2013) DOI10.1063/1.4825706
  2. Aktaş, R., A note on multivariable Humbert matrix polynomials, Gazi Univ. J. Sci. 27 (2014), 747-754. (2014) 
  3. Aktaş, R., Çekim, B., Çevik, A., Extended Jacobi matrix polynomials, Util. Math. 92 (2013), 47-64. (2013) MR3136666
  4. Aktaş, R., Çekim, B., Şahin, R., 10.18514/MMN.2012.356, Miskolc Math. Notes 13 (2012), 197-208. (2012) Zbl1274.33009MR3002623DOI10.18514/MMN.2012.356
  5. Altın, A., Çekim, B., Generating matrix functions for Chebyshev matrix polynomials of the second kind, Hacet. J. Math. Stat. 41 (2012), 25-32. (2012) Zbl1259.33014MR2976908
  6. Altın, A., Çekim, B., Some properties associated with Hermite matrix polynomials, Util. Math. 88 (2012), 171-181. (2012) Zbl1262.15023MR2975830
  7. Altın, A., Çekim, B., Some miscellaneous properties for Gegenbauer matrix polynomials, Util. Math. 92 (2013), 377-387. (2013) Zbl1293.33007MR3136694
  8. Çekim, B., Altın, A., Aktaş, R., Some relations satisfied by orthogonal matrix polynomials, Hacet. J. Math. Stat. 40 (2011), 241-253. (2011) Zbl1229.33012MR2839191
  9. Çekim, B., Altın, A., Aktaş, R., 10.2298/FIL1304713C, Filomat 27 (2013), 713-719. (2013) MR3243979DOI10.2298/FIL1304713C
  10. Defez, E., Jódar, L., 10.1016/S0377-0427(98)00149-6, J. Comput. Appl. Math. 99 (1998), 105-117. (1998) Zbl0929.33006MR1662687DOI10.1016/S0377-0427(98)00149-6
  11. Defez, E., Jódar, L., Chebyshev matrix polynomials and second order matrix differential equations, Util. Math. 61 (2002), 107-123. (2002) Zbl0998.15034MR1899321
  12. Defez, E., Jódar, L., Law, A., 10.1016/j.camwa.2004.01.011, Comput. Math. Appl. 48 (2004), 789-803. (2004) Zbl1069.33007MR2105252DOI10.1016/j.camwa.2004.01.011
  13. Dunford, N., Schwartz, J. T., Linear Operators. Part I, General Theory, Pure and Applied Mathematics 7 A Wiley-Interscience Publishers, John Wiley & Sons, New York (1958). (1958) MR1009162
  14. James, A. T., Special functions of matrix and single argument in statistics, Theory and Application of Special Functions, Proc. Advanced Sem., Math. Res. Center, Madison, Wis. R. A. Askey Academic Press, New York (1975), 497-520. (1975) Zbl0326.33010MR0402145
  15. Jódar, L., Company, R., Hermite matrix polynomials and second order matrix differential equations, Approximation Theory Appl. 12 (1996), 20-30. (1996) MR1465570
  16. Jódar, L., Company, R., Ponsoda, E., Orthogonal matrix polynomials and systems of second order differential equations, Differ. Equ. Dyn. Syst. 3 (1995), 269-288. (1995) Zbl0892.33004MR1386749
  17. Jódar, L., Cortés, J. C., 10.1016/S0377-0427(98)00158-7, J. Comput. Appl. Math. 99 (1998), 205-217. (1998) Zbl0933.33004MR1662696DOI10.1016/S0377-0427(98)00158-7
  18. Jódar, L., Cortés, J. C., 10.1016/S0895-7177(00)00187-4, Math. Comput. Modelling 32 (2000), 1017-1028. (2000) Zbl0985.33006MR1799616DOI10.1016/S0895-7177(00)00187-4
  19. Jódar, L., Defez, E., On Hermite matrix polynomials and Hermite matrix functions, Approximation Theory Appl. 14 (1998), 36-48. (1998) MR1651470
  20. Jódar, L., Sastre, J., On Laguerre matrix polynomials, Util. Math. 53 (1998), 37-48. (1998) Zbl0990.33008MR1622055
  21. Kargin, L., Kurt, V., Some relations on Hermite matrix polynomials, Math. Comput. Appl. 18 (2013), 323-329. (2013) MR3113139
  22. Khammash, G. S., Shehata, A., On Humbert matrix polynomials, Asian J. Current Eng. Maths. 1 (2012), 232-240 http://innovativejournal.in/index.php/ajcem/article/view/104/96. (2012) 
  23. Khan, S., Hassan, N. A. Makboul, 10.1088/1751-8113/43/23/235204, J. Phys. A, Math. Theor. 43 (2010), Article ID 235204, 21 pages. (2010) MR2646680DOI10.1088/1751-8113/43/23/235204
  24. Metwally, M. S., Mohamed, M. T., Shehata, A., On Hermite-Hermite matrix polynomials, Math. Bohem. 133 (2008), 421-434. (2008) Zbl1199.15079MR2472489
  25. Sastre, J., Jódar, L., On Laguerre matrix polynomial series, Util. Math. 71 (2006), 109-130. (2006) Zbl1106.33011MR2278826
  26. Shehata, A., On Tricomi and Hermite-Tricomi matrix functions of complex variable, Commun. Math. Appl. 2 (2011), 97-109. (2011) Zbl1266.33012MR3000027
  27. Shehata, A., A new extension of Gegenbauer matrix polynomials and their properties, Bull. Int. Math. Virtual Inst. 2 (2012), 29-42. (2012) MR3149829
  28. Shehata, A., On pseudo Legendre matrix polynomials, Int. J. Math. Sci. Eng. Appl. 6 (2012), 251-258. (2012) MR3057762
  29. Shehata, A., On Rainville's matrix polynomials, Sylwan J. 158 (2014), 158-178. (2014) MR3248615
  30. Shehata, A., 10.1007/s13370-013-0149-3, Afr. Mat. 25 (2014), 757-777. (2014) Zbl1321.15041MR3248615DOI10.1007/s13370-013-0149-3
  31. Shehata, A., 10.9734/BJMCS/2015/11492, British Journal of Mathematics and Computer Science 5 (2015), 92-102 10.9734/BJMCS/2015/11492. (2015) DOI10.9734/BJMCS/2015/11492
  32. Shehata, A., On a new family of the extended generalized Bessel-type matrix polynomials, Mitteilungen Klosterneuburg J. 65 (2015), 100-121. (2015) 
  33. Shehata, A., On modified Laguerre matrix polynomials, J. Nat. Sci. Math. 8 (2015), 153-166. (2015) MR3404349
  34. Taşdelen, F., Çekim, B., Aktaş, R., 10.1016/j.camwa.2011.02.019, Comput. Math. Appl. 61 (2011), 2412-2423. (2011) Zbl1221.33022MR2794989DOI10.1016/j.camwa.2011.02.019
  35. Upadhyaya, L. M., Shehata, A., On Legendre matrix polynomials and its applications, Int. Trans. Math. Sci. Comput. 4 (2011), 291-310. (2011) MR3057762
  36. Upadhyaya, L. M., Shehata, A., 10.1007/s40840-014-0010-3, Bull. Malays. Math. Sci. Soc. (2) 38 (2015), 165-179. (2015) Zbl1311.33008MR3394046DOI10.1007/s40840-014-0010-3
  37. Varma, S., Çekim, B., Yeşildal, F. Taşdelen, On Konhauser matrix polynomials, Ars Comb. 100 (2011), 193-204. (2011) MR2798172
  38. Varma, S., Taşdelen, F., 10.1016/j.camwa.2011.08.063, Comput. Math. Appl. 62 (2011), 3663-3668. (2011) Zbl1236.15048MR2852088DOI10.1016/j.camwa.2011.08.063

NotesEmbed ?

top

You must be logged in to post comments.