### Connections between Legendre with Hermite and Laguerre Matrix Polynomials

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Aktas, R. A note on multivariable Humbert matrix polynomials. Gazi University Journal of Science, 27 (2) (2014), 747-754.

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

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

Çekim, B., Altin, A., and Aktas, R. Some new results for Jacobi matrix polynomials. Filomat, 27 (4) (2013), 713-719

Defez, E., and Jódar, L. Some applications of the Hermite matrix polynomials series expansions. J. Comp. Appl. Math., 99 (1998), 105-117.

Dunford, N., and Schwartz, J.T. Linear Operators, part I, General Theory. Interscience Publishers, INC. New York, 1957.

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

Jódar, L., and Company, R. Hermite matrix polynomials and second order matrix differential equations. J. Approx. Theory Appl., 12 (1996), 20-30.

Jódar, L. Company, R., and Navarro, E. Laguerre matrix polynomials and system of second-order differential equations. Appl. Num. Math., 15 (1994), 53-63.

Jódar, L., and Defez, E. A connection between Laguerre’s and Hermite’s matrix polynomials. Appl. Math. Lett., 11 (1998), 13-17.

Jódar, L., and Defez, E. On Hermite matrix polynomials and Hermite matrix function. J. Approx. Theory Appl., 14 (1998), 36-48.

Jódar, L., and Sastre, J. On Laguerre matrix polynomials. Utilitas Math., 53 (1998), 37-48.

Metwally, M.S., Mohamed, M.T., and Shehata, A. On Hermite-Hermite Bohemica. 133 (4) (2008), 421-434. polynomials. Math.

Metwally, M.S., Mohamed, M.T., and Shehata, A. Generalizations of two-index two-variable Hermite matrix polynomials. Demonstratio Mathematica, 42 (2009), 687-701.

Rainville, E.D. Special Functions. The Macmillan Company, New York, 1960.

Shehata, A. On Tricomi and Hermite-Tricomi matrix functions of complex variable. Communications Math. Applications, 2 (2-3) (2011), 97-109.

Shehata, A. A new extension of Hermite-Hermite matrix polynomials and their properties. Thai Journal of Mathematics, 10 (2) (2012), 433-444.

Shehata, A. A new extension of Gegenbauer matrix polynomials and their properties. Bulletin Inter. Math. Virtual Institute, 2 (2012), 29-42.

Shehata, A. On Rice’s matrix polynomials. Afrika Matematika, 25 (3) (2014), 757-777.

Shehata, A. On Rainville’s matrix polynomials. Sylwan Journal, 158 (9) (2014), 158-178.

Shehata, A. Some relations on Humbert matrix polynomials. Mathematica Bohemica, (in press).

Shehata, A. Some relations on Konhauser matrix polynomials. Miskolc Mathematical Notes, (in press).

Shehata, A. New kinds of Hypergeometric matrix functions. British Journal of Mathematics and Computer Science, 5 (1) (2015), 92-102.

Shehata, A. On a new family of the extended generalized Mitteilungen Klosterneuburg Journal, 65 (2) (2015), 100-121. matrix polynomials.

Upadhyaya, L.M., and Shehata, A. On Legendre matrix polynomials and its applications. Inter. Trans. Mathematical Sci. Computer (ITMSC), 4 (2) (2011), 291-310.

Upadhyaya, L.M., and Shehata, A. A new extension of generalized Hermite matrix polynomials. Bulletin Malaysian Mathematical Sci. Soc., 38 (1) (2015), 165–179.

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