Generating relations involving 2-variable Hermite matrix polynomials

Ahmed Ali Al-Gonah

doi:10.26637/mjm203/008

Abstract

In the present paper, some generating relations involving the 2-variable Hermite matrix polynomials are derived by using operational techniques. Further, some new and known generating relations for the scalar Hermite polynomials are obtained as applications of the main results.

Keywords:

Hermite matrix polynomials, Generating relations

Mathematics Subject Classification:

15A60, 33C05, 33C25, 33C45, 33C50

Authors Imprint References Funding Related Articles Downloads

Ahmed Ali Al-Gonah Department of Mathematics, Aden University, Aden, Yemen

Pages: 236-242
Date Published: 01-07-2014
Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)

P. Appell, Kampé de Fériet J., Fonctions hypergéométriques et hypersph-ériques: Polynômes d’ Hermite, Gauthier-Villars, Paris, 1926.

R.S. Batahan, A new extension of Hermite matrix polynomials and its applications, Linear Algebra Appl. 419 (2006), 82-92. DOI: https://doi.org/10.1016/j.laa.2006.04.006

R.S. Batahan, Volterra integral equation of Hermite matrix polynomials, Anal. Theory Appl. 29 (2) (2013), 97–103. DOI: https://doi.org/10.4208/ata.2013.v29.n2.1

G. Dattoli, Hermite-Bessel and Laguerre-Bessel functions: a by product of the monomiality principle. Advanced special functions and applications (Melfi, 1999), 147-164, Proc. Melfi Sch. Adv. Top. Math. Phys., 1, Aracne, Rome, (2000).

G. Dattoli, Generalized polynomials, operational identities and their applications, J. Comput. Appl. Math. 118 (2000), 111-123. DOI: https://doi.org/10.1016/S0377-0427(00)00283-1

G. Dattoli, Subuhi Khan, P. E. Ricci, On Crofton-Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case. Integral Transforms Spec. Funct. 19 (1) (2008), 1–9. DOI: https://doi.org/10.1080/10652460701358984

G. Dattoli, P.L. Ottaviani , A. Torre, L. Vázquez, Evolution operator equations: integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory, Riv. Nuovo Cimento Soc. Ital. Fis.(4) 20 (1997), 1-133. DOI: https://doi.org/10.1007/BF02907529

G. Dattoli, A. Torre, S. Lorenzutta, Operational identities and properties of ordinary and generalized special functions, J. Math. Anal. Appl. 236 (1999), 399–414. DOI: https://doi.org/10.1006/jmaa.1999.6447

E. Defez, A. Hervás, L. Jódar, Bounding Hermite matrix polynomials, Math. Comput. Modelling 40 (2004) 117-125. DOI: https://doi.org/10.1016/j.mcm.2003.11.004

E. Defez, L. Jódar, Some applications of the Hermite matrix polynomials series expansions, J. Comput. Appl. Math. 99 (1998), 105-117. DOI: https://doi.org/10.1016/S0377-0427(98)00149-6

N. Dunford, J. Schwartz, Linear operators, Part I, Interscience, New York, 1957.

L. Jódar, R. Company, Hermite matrix polynomials and second order matrix differential equations, Approx. Theory Appl. (N.S.) 12 (1996), 20-30. DOI: https://doi.org/10.1007/BF02836202

L. Jódar, E. Defez, A matrix formula for the generating function of the product of Hermite matrix polynomials, In International Workshop on Orthogonal Polynomials in Mathematical Physics, (1996) 93–101.

L. Jódar, E. Defez, On Hermite matrix polynomials and Hermite matrix functions, Approx. Theory Appl. (N.S.) 14 (1998), 36-48. DOI: https://doi.org/10.1007/BF02836885

Subuhi Khan, N. Raza, 2-variable generalized Hermite matrix polynomials and Lie algebra representation, Rep. Math. Phys. 66 (2010), 159-174. DOI: https://doi.org/10.1016/S0034-4877(10)00024-8

M. S. Metwally, M. T. Mohamed, A. Shehata, Generalizations of two-index two-variable Hermite matrix polynomials, Demonstratio Math. 42 (2009), 687-701. DOI: https://doi.org/10.1515/dema-2013-0207

M. I. Qureshi, Yasmeen, M. A. Pathan, Linear and bilinear generating functions involving Gould-Hopper polynomials, Math. Sci. Res. J. 6 (9) (2002), 449–456.

E.D. Rainville, Special functions, Reprint of 1960 first edition, Chelsea Publishing Co., Bronx, New York, 1971.

K.A.M. Sayyed, M.S. Metwally, R.S. Batahan, On generalized Hermite matrix polynomials, Electron. J. Linear Algebra 10 (2003), 272-279. DOI: https://doi.org/10.13001/1081-3810.1113

M.J.S. Shahwan, M.A. Pathan, Generating relations of Hermite matrix polynomials by Lie algebraic method, Ital. J. Pure Appl. Math. 25 (2009), 187–192.