Closed form general solution of the hypergeometric matrix differential equation. (English) Zbl 0985.33006

The authors have studied hypergeometric matrix differential equation and its connection with the hypergeometric matrix function. Some properties about hypergeometric matrix function such as invertibility, error bounds for its truncated series expansion and bounds for its inverse and its derivative in terms of the date are given.


33C47 Other special orthogonal polynomials and functions
Full Text: DOI


[1] Lebedev, N.N., Special functions and their applications, (1972), Dover New York · Zbl 0271.33001
[2] Luke, Y.L., ()
[3] Muirhead, R.J., Systems of partial differential equations for hypergeometric functions of matrix argument, Ann. math. statist., 41, 991-1001, (1970) · Zbl 0225.62078
[4] Rainville, E.D., Special functions, (1960), Chelsea New York · Zbl 0050.07401
[5] Constantine, A.G.; Muirhead, R.J., Partial differential equations for hypergeometric functions of two arguments matrices, J. multivariate anal., 3, 332-338, (1972) · Zbl 0256.33007
[6] James, A.T., Special functions of matrix and single argument in statistics, (), 497-520
[7] Durán, A.J.; López-Rodríguez, P., Orthogonal matrix polynomials: zeros and Blumenthal’s theorem, J. of approx. theory, 84, 96-118, (1996) · Zbl 0861.42016
[8] Jódar, L.; Company, R.; Navarro, E., Laguerre matrix polynomials and systems of second-order differential equations, Applied numer. math., 15, 53-63, (1994) · Zbl 0821.34010
[9] Jódar, L.; Company, R., Hermite matrix polynomials and second order matrix differential equations, Approximation theory appl., 12, 2, 20-30, (1996) · Zbl 0858.15014
[10] Jódar, L.; Company, R.; Ponsoda, E., Orthogonal matrix polynomials and systems of second order differential equations, Diff. equations & dynam. syst., 3, 3, 269-298, (1995) · Zbl 0892.33004
[11] Golub, G.; Van Loan, C.F., Matrix computations, (1991), The Johns Hopkins Univ. Press Baltimore, MD
[12] Dunford, N.; Schwartz, J., Linear operators, (1957), Interscience New York, Part I
[13] Dieudonné, J., Foundations of modern analysis, (1960), Academic Press New York · Zbl 0100.04201
[14] Jódar, L., Explicit solutions for second order operator differential equations with two boundary value conditions, Linear algebra appl., 103, 73-86, (1988) · Zbl 0651.34062
[15] Saks, S.; Zygmund, A., Analytic functions, (1971), Elsevier Amsterdam · JFM 60.0243.01
[16] Brezinski, C., Other manifestations of the Schur complement, Linear algebra appl., 111, 231-247, (1988) · Zbl 0662.65037
[17] Temme, N.M., Special functions, (1996), John Wiley & Sons New York · Zbl 0863.33002
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.