×

Biorthogonal matrix polynomials related to Jacobi matrix polynomials. (English) Zbl 1236.15048

Summary: We define the pair of biorthogonal matrix polynomials suggested by the Jacobi matrix polynomials. Biorthogonality property, matrix generating functions and matrix recurrence relations are given.

MSC:

15A54 Matrices over function rings in one or more variables
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Defez, E.; Jódar, L.; Law, A., Jacobi matrix differential equation, polynomial solutions and their properties, Comput. math. appl., 48, 789-803, (2004) · Zbl 1069.33007
[2] Defez, E.; Jódar, L., Some applications of the Hermite matrix polynomials series expansions, J. comput. appl. math., 99, 105-117, (1998) · Zbl 0929.33006
[3] Defez, E.; Jódar, L., Chebyshev matrix polynomials and second order matrix differential equations, Util. math., 61, 107-123, (2002) · Zbl 0998.15034
[4] Jódar, L.; Company, R., Hermite matrix polynomials and second order matrix differential equations, Approx. theory appl., 12, 2, 20-30, (1996) · Zbl 0858.15014
[5] Jódar, L.; Company, R.; Navarro, E., Laguerre matrix polynomials and system of second-order differential equations, Appl. numer. math., 15, 53-63, (1994) · Zbl 0821.34010
[6] Jódar, L.; Company, R.; Ponsoda, E., Orthogonal matrix polynomials and systems of second order differential equations, Differ. equ. dyn. syst., 3, 269-288, (1996) · Zbl 0892.33004
[7] Jódar, L.; Defez, E.; Ponsoda, E., Orthogonal matrix polynomials with respect to linear matrix moment functionals: theory and applications, J. approx. theory appl., 12, 1, 96-115, (1996) · Zbl 0853.42022
[8] Sayyed, K.A.M.; Metwally, M.S.; Batahan, R.S., Gegenbauer matrix polynomials and second order matrix differential equations, Divulg. mat., 12, 2, 101-115, (2004) · Zbl 1102.33010
[9] Geronimo, J.S., Scattering theory and matrix orthogonal polynomials on the real line, Circuit systems signal process., 1, 3-4, 471-494, (1982) · Zbl 0506.15010
[10] Varma, S.; Çekim, B.; Taşdelen, F., On konhauser matrix polynomials, Ars combin., 100, 193-204, (2011) · Zbl 1265.33027
[11] Madhekar, H.C.; Thakare, N.K., Biorthogonal polynomials suggested by the Jacobi polynomials, Pacific J. math., 100, 417-424, (1982) · Zbl 0456.33009
[12] Dunford, N.; Schwartz, J., Linear operators. vol. I, (1957), Interscience New York
[13] Jódar, L.; Cortés, J.C., Some properties of gamma and beta matrix functions, Appl. math. lett., 11, 1, 89-93, (1998) · Zbl 1074.33002
[14] Jódar, L.; Cortés, J.C., On the hypergeometric matrix function, J. comput. appl. math., 99, 205-217, (1998) · Zbl 0933.33004
[15] Carlitz, L., A note on certain biorthogonal polynomials, Pacific J. math., 24, 425-430, (1968) · Zbl 0157.11902
[16] A. Altın, B. Çekim, E. Duman, Families of generating functions for the Jacobi and related matrix polynomials. Ars Combin. (in press).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.