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

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DOI: 10.4236/apm.2014.47043    2,480 Downloads   2,836 Views   Citations

ABSTRACT

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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Khammash, G. and Shehata, A. (2014) Reply to Comment on “On Humbert Matrix Polynomials of Two Variables”. Advances in Pure Mathematics, 4, 324-325. doi: 10.4236/apm.2014.47043.

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.

  
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