A Note on Multivariable Humbert Matrix Polynomials

Rabia AKTAŞ
1.983 855

Abstract


In this paper, we deal with some properties of the matrix extension of the multivariable Humbert polynomials defined by Aktas et.al [Aktaş, R., Çekim, B. and Şahin, R., The matrix version for the multivariable Humbert polynomials, Miskolc Mathematical Notes, 13(2) (2012), 197-208]. We give matrix differential equations for the products of these matrix polynomials and some other multivariable matrix polynomials, and also we present some new relations for the multivariable Humbert matrix polynomials.

Keywords


Multivariable Humbert matrix polynomials, Chan-Chyan-Srivastava matrix polynomials, Erkus-Srivastava matrix polynomials, multivariable Lagrange-Hermite matrix polynomials, matrix differential equation

Full Text:

PDF

References


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).