Approximation of hypergeometric functions with matricial argument through their development in series of zonal polynomials

Electronic Transactions on Numerical Analysis

Volumn 11, Issue , 2000, Pages 121-130

  Gutierrez R ^a   Rodriguez, J ^b   Saez A J ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITY OF JAÉN   (Spain)

Author keywords

Hypergeometric functions with matricial argument; Zonal polynomials

Indexed keywords

EID: 1342277438     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. S. BOCHNER, Bessel functions and modular relations of higher type and hyperbolic differential equations, Comm. Sém. Math. Univ. Lund, Tome Supplementaire (1952), pp. 12-20.
2. A. G. CONSTANTINE, Some non-central distribution problems in multivariate analysis, Ann. Math. Statist., 34 (1963), pp. 1270-1285.
3. S. G. GINDIKIN, Analysis on homogeneous spaces, Russian Math. Surveys, 19 (1964), pp. 1-90.
4. K. I. GROSS AND D. ST. P. RICHARDS, Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions, Trans. Amer. Math. Soc., 301 (1987), no. 2, pp. 781-811.
5. 1 function of matricial argument, in Applied Stochastics Models and Data Analysis, Proc. IX International Symp. Lisboa, H Barcelar-Nicolau, F. Costa-Nicolau, and J. Jansen, eds., pp. 194-199, I.N.E., Portugal, 1999.
6. C. S. HERZ, Bessel functions of matricial argument, Ann. of Math., 61 (1955), pp. 474-523.
7. A. T JAMES, Distributions of matrix variates and latent roots derived from normal samples, Ann. Math. Statist., 35 (1964), pp. 475-501.
8. _. Calculation of zonal polynomial coefficient by use of the Laplace-Beltrami operator, Ann. Math. Statist., 39 (1968), pp. 1711-1718.
9. R. J. MUIRHEAD, Aspects of multivariate statistical theory, John Wiley & Sons, Inc., New York, 1982.
10. J. RODRIGUEZ, A. J. SAEZ, Generación de distribuciones multivariates discretas mediante el uso de polinomios zonales, in Proc. of XXIV Congreso Nacional de Estadística e Investigación Operativa, SEIO España, 1998.
11. A. SELBERG, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet spaces, J. Indian Math. Soc., 20 (1956), pp. 47-87.
12. G. SHIMURA, Confluent hypergeometric functions on tube domains, Math. Ann., 260 (1982), pp. 269-302.
13. C. L. SIEGEL, Über die analytische Theorie der quadratischen Formen. I, Ann. of Math. (2), 36 (1935), pp. 527-608.
14. A. TAKEMURA, Zonal polynomials, Institute of Mathematical Statistics Lecture Notes, Monograph Series, vol. 4, Institute of Mathematical Statistics, Hayward, California, 1984.
15. A. TERRAS , Special functions for the symmetric space of positive matrices, SIAM J. Math. Anal., 16 (1985), pp. 620-640.