Reply to Comment on “On Humbert Matrix Polynomials of Two Variables”

Ghazi S. Khammash, Ayman Shehata

Department of Mathematics, Al-Aqsa University, Gaza Strip, Palestine.
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.

DOI: 10.4236/apm.2014.47043                

Abstract

The formula subject to comment in Reference [1] is correct.

Keywords

Matrix Functions, Humbert Matrix Polynomials

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Khammash, G.S. and Shehata, A. (2012) On Humbert Matrix Polynomials of Two Variables. Advances in Pure Mathematics, 2, 423-427. http://dx.doi.org/10.4236/apm.2012.26064
[2]	Basauri, V.S. (2013) A Comment on “On Humbert Matrix Polynomials of Two Variables”. Advances in Pure Mathematics, 3, 470-471. http://dx.doi.org/10.4236/apm.2013.35066
[3]	Basauri, V.S. (2013) A Study of a Two Variables Gegenbauer Matrix Polynomials and Second Order Matrix Partial Differential Equations. A comment. International Journal of Mathematical Analysis, 7, 973-976.
[4]	Jódar, L., Company, R. and Ponsoda, E. (1995) Orthogonal Matrix Polynomials and Systems of Second Order Differential Equations. Differential Equations and Dynamical Systems, 3, 269-288.
[5]	Jódar, L. and Cortés, J.C. (1998) On the Hypergeometric Matrix Functions. Journal of Computational and Applied Mathematics, 99, 205-217. http://dx.doi.org/10.1016/S0377-0427(98)00158-7
[6]	Aktas, R., Cekim, B. and Sahin, R. (2012) The Matrix Version for the Multivariable Humbert Polynomials. Miskolc Mathematical Notes, 13, 197-208.
[7]	Kahmmash, G.S. (2008) A Study of a Two Variables Gegenbauer Matrix Polynomials and Second Order Matrix Partial Differential Equations. International Journal of Mathematics Analysis, 2, 807-821.
[8]	Dattoli, G., Ricci, P.E. and Srivastava, H.M. (2003) Two-Index Multidimensional Gegenbauer Polynomials and Their Integral Representations. Mathematical and Computer Modelling, 37, 283-291. http://dx.doi.org/10.1016/S0895-7177(03)00006-2
[9]	Pathan, M.A. and Khan, M.A. (1997) On Polynomials Associated with Humbert’s Polynomials. Publ. Inst. Math. (Beograd) (N.S.), 67, 53-62.