Keywords
zonal polynomials
Hermitian matrix
Legendre’s differential equation
Operador de Laplace-Beltrami
polinomios zonales
matriz hermitiana
ecuación diferencial de Legendre
How to Cite
Abstract
A formula for complex zonal polynomials of second order is derived by solving a particular partial differential equation.
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.