Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
A formula for complex zonal polynomials of second order
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Keywords

Laplace-Beltrami operator
zonal polynomials
Hermitian matrix
Legendre’s differential equation
Operador de Laplace-Beltrami
polinomios zonales
matriz hermitiana
ecuación diferencial de Legendre

How to Cite

Caro-Lopera, F. J., González-Farías, G., & Díaz-García, J. A. (2006). A formula for complex zonal polynomials of second order. Revista De Matemática: Teoría Y Aplicaciones, 13(1), 35–39. https://doi.org/10.15517/rmta.v13i1.266

Abstract

A formula for complex zonal polynomials of second order is derived by solving a particular partial differential equation.

https://doi.org/10.15517/rmta.v13i1.266
PDF (Español (España))

References

Dı́az-García, J.A.; Caro, F.J. (2006a) “An alternative approach for deriving the Laplace-Beltrami operator for the zonal polynomials of positive semidefinite and definite matrix argument”, Far East Journal of Mathematical Sciences (FJMS) 22(3): 273–290.

Dı́az- García, J.A.; Caro, F.J. (2006b) “Derivation of the Laplace-Beltrami operator for the zonal polynomials of positive definite Hermitian matrix argument”. Submitted.

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F.; Bertin, D.; Fulks, W.; Harvey, A.; Thomsen, D.; Weber, M.; Whitney E. (1981) Higher Trascendeltal Functions 1. Robert E. Krieger Publishing Company, Malabar.

Farrell R.H. (1980) “Calculation of complex zonal polynomials”, in: P.R. Kishnaiah (Ed.) Multivariate Analysis V, North Holland: 301–320.

James, A. T. (1968) “Calculation of zonal polynomial coefficients by use of the Laplace-Beltrami operator”, Ann. Math. Statist. 39: 1711–1718.

Khatri, C. G. (1907) “On the moments of traces of two matrices in three situations for complex multivariate normal populations”, Sankhyā, A 32: 65–80.

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