A formula for Jack polynomials of the second order

Volume 34 / 2007

Francisco J. Caro-Lopera, José A. Díaz-García, Graciela González-Farías Applicationes Mathematicae 34 (2007), 113-119 MSC: 05E05, 35M99, 33C05. DOI: 10.4064/am34-1-9

Abstract

This work solves the partial differential equation for Jack polynomials $C_{\kappa }^{\alpha }$ of the second order. When the parameter $\alpha $ of the solution takes the values $1/2, 1$ and $2$ we get explicit formulas for the quaternionic, complex and real zonal polynomials of the second order, respectively.

Authors

  • Francisco J. Caro-LoperaDepartment of Basic Mathematics
    Centro de Investigación en Matemáticas
    Callejón de Jalisco s//n
    Mineral de Valenciana
    36240 Guanajuato, Guanajuato, México
    e-mail
  • José A. Díaz-GarcíaDepartment of Statistics and Computation
    Universidad Autónoma Agraria Antonio Narro
    25315 Buenavista Saltillo, Coahuila, México
    e-mail
  • Graciela González-FaríasDepartment of Statistics
    Centro de Investigación en Matemáticas
    Callejón de Jalisco s//n
    Mineral de Valenciana
    36240 Guanajuato, Guanajuato, México
    e-mail

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