### A Note on Multivariable Humbert Matrix Polynomials

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Aktaş, R., "Some new results for the multivariable Humbert polynomials", Mathematica Slovaca, In press.

Aktaş, R., "A new multivariable extension of Humbert matrix polynomials", AIP Conf. Proc., 1558: 1128, (2013).

Aktaş, R., Çekim, B. and Çevik, A., "Extended Jacobi matrix polynomials", Utilitas Mathematica, 92: 47- 64, (2013).

Aktaş, R., Çekim, B. and Şahin, R., "The matrix version for the multivariable Humbert polynomials", Miskolc Mathematical Notes, 13(2): 197-208, (2012).

Aktaş, R., Şahin, R. and Altın, A., "On a multivariable extension of the Humbert polynomials", Applied Mathematics and Computation, 218(3): 662-666, (2011).

Altın, A. and Çekim, B., "Generating matrix functions for Chebyshev matrix polynomials of the second kind", Hacettepe Journal of Mathematics and Statistics, 41(1): 25-32, (2012).

Altın, A. and Çekim, B., "Some properties associated with Mathematica, 88: 171-181, (2012). polynomials", Utilitas

Altın, A. and Çekim, B., "Some miscellaneous properties for Gegenbauer matrix polynomials", Utilitas Mathematica, 92: 377-387, (2013).

Altın, A. and Erkuş, E., "On a multivariable extension of the Lagrange-Hermite polynomials", Integral Transforms and Special Functions, 17: 239-244, (2006).

Chan, W.-C. C., Chyan, C.-J. and Srivastava, H. M., "The Lagrange polynomials in several variables", Integral Transforms and Special Functions, 12: 139-148, (2001).

Çekim, B., Altın, A. and Aktaş, R., "Some relations satisfied Hacettepe Journal of Mathematics and Statistics, 40(2): 241-253, (2011). matrix polynomials",

Çekim, B, Altın, A. and Aktaş, R., "Some new results for Jacobi matrix polynomials", Filomat, 27 (4): 713- 719, (2013).

Çekim, B. and Erkuş-Duman, E., "On the g-Jacobi matrix functions", Advances in Applied Mathematics and Approximation Theory, Springer Proceedings in Mathematics and Statistics, 73-84, (2013).

Çekim, B. and Erkuş-Duman, E., "Integral Representations for Bessel Matrix Functions", Gazi University Journal of Science, 27(1): 663-667, (2014).

Defez, E. and Jódar, L., "Chebyshev matrix polynomials and second order matrix differential equations", Utilitas Mathematica, 61: 107-123, (2002).

Defez, E., Jódar, L. and Law, A., "Jacobi matrix differential equation, polynomial solutions and their properties", Computers and Mathematics with Applications, 48: 789-803, (2004).

Defez, E., Jódar, L., Law, A. and Ponsoda, E., "Three- term recurrences and matrix orthogonal polynomials", Utilitas Mathematica, 57: 129-146, (2000).

Defez, E., Law, A., Villanueva-Oller, J. and Villanueva, R.J., "Matrix cubic splines for progressive 3D imaging", Journal of Mathematical Imaging and Vision, 17: 41-53, (2002).

Dunford, N. and Schwartz, J., "Linear Operators", Vol. I, Interscience, New York, (1957).

Duran, A.J., "On orthogonal polynomials with respect to a positive definite matrix of measures", Canadian Journal of Mathematics, 47: 88-112, (1995).

Duran, A.J. and Lopez-Rodriguez, P., "Orthogonal matrix theorem", Journal of Approximation Theory, 84: 96- 118, (1996). and Blumenthal's

Erkuş-Duman, E., "Matrix extensions of polynomials in several variables", Utilitas Mathematica, 85: 161- 180, (2011).

Erkuş-Duman, E., Altın, A. and Aktaş, R., "Miscellaneous properties of some multivariable polynomials", Modelling, 54(9-10): 1875-1885, (2011). and Computer

Erkuş, E. and Srivastava, H. M., "A unified presentation of some families of multivariable polynomials", Integral Transforms and Special Functions, 17: 267-273, (2006).

Geronimo, J.S., "Scattering theory and matrix orthogonal polynomials on the real line", Circuit Systems Signal Process, 1 (3-4): 471-494, (1982).

Gould, H. W., "Inverse series relation and other expansions involving Humbert polynomials", Duke Mathematical Journal, 32: 697-711, (1965).

James, A.T., "Special functions of matrix and single argument in statistics, In Theory and Applications of Special Functions", Academic Press, (Edited by R.A. Askey), 497-520, (1975).

Jódar, L. and Company, R., "Hermite matrix polynomials and second order matrix differential equations", Applications, 12(2): 20--30, (1996). Theory and its

Jódar, L., Company, R. and Navarro, E., "Laguerre matrix polynomials and system of second-order differential Mathematics, 15: 53--63, (1994). Applied Numerical

Jódar, L., Company, R. and Ponsoda, E., "Orthogonal matrix polynomials and systems of second order differential equations", Differential Equations and Dynamical Systems, 3: 269-288, (1996).

Jódar, L. and Cortés, J.C., "On the hypergeometric matrix function", Journal of Computational and Applied Mathematics, 99: 205-217, (1998).

Jódar, L. and Cortés, J.C., "Some properties of Gamma and Beta matrix functions", Applied Mathematics Letters, 11(1): 89-93, (1998).

Jódar, L., Defez, E. and Ponsoda, E., "Matrix quadrature and orthogonal matrix polynomials", Congressus Numerantium, 106: 141-153, (1995).

Khammash, Ghazi S. and Shehata, A., "On Humbert matrix polynomials", Asian Journal of Current Engineering and Maths, 1: 232-240, (2012).

Lee, D.W., "Partial differential equations for products of two classical orthogonal polynomials", Bulletin of the Korean Mathematical Society, 42: 179-188, (2005).

Sinap, A. and Van Assche, W., "Polynomial interpolation and Gaussian quadrature for matrix valued Applications, 207: 71-114, (1994). Algebra and its

Taşdelen, F., Çekim, B. and Aktaş, R., "On a multivariable polynomials", J. Comput. Math. Appl., 61(9): 2412- 2423, (2011). of Jacobi matrix

Varma, S., Çekim, B. and Taşdelen, F., "On Konhauser matrix polynomials", Ars Combinatoria, 100: 193-204, (2011).