Geodesic
A formula for Jack polynomials of the second order
Francisco J. Caro-Lopera1 ; José A. Díaz-García2 ; Graciela González-Farías3
1 Department of Basic Mathematics Centro de Investigación en Matemáticas Callejón de Jalisco s//n Mineral de Valenciana 36240 Guanajuato, Guanajuato, México
2 Department of Statistics and Computation Universidad Autónoma Agraria Antonio Narro 25315 Buenavista Saltillo, Coahuila, México
3 Department of Statistics Centro de Investigación en Matemáticas Callejón de Jalisco s//n Mineral de Valenciana 36240 Guanajuato, Guanajuato, México
Applicationes Mathematicae, Tome 34 (2007) no. 1, pp. 113-119 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am34-1-9
Keywords: work solves partial differential equation jack polynomials kappa alpha second order parameter alpha solution takes values get explicit formulas quaternionic complex real zonal polynomials second order respectively

Francisco J. Caro-Lopera 1 ; José A. Díaz-García 2 ; Graciela González-Farías 3

1 Department of Basic Mathematics Centro de Investigación en Matemáticas Callejón de Jalisco s//n Mineral de Valenciana 36240 Guanajuato, Guanajuato, México
2 Department of Statistics and Computation Universidad Autónoma Agraria Antonio Narro 25315 Buenavista Saltillo, Coahuila, México
3 Department of Statistics Centro de Investigación en Matemáticas Callejón de Jalisco s//n Mineral de Valenciana 36240 Guanajuato, Guanajuato, México 
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     author = {Francisco J. Caro-Lopera and Jos\'e A. D{\'\i}az-Garc{\'\i}a and Graciela Gonz\'alez-Far{\'\i}as},
     title = {A formula for {Jack} polynomials
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     journal = {Applicationes Mathematicae},
     pages = {113--119},
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     doi = {10.4064/am34-1-9},
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Francisco J. Caro-Lopera; José A. Díaz-García; Graciela González-Farías. A formula for Jack polynomials
 of the second order. Applicationes Mathematicae, Tome 34 (2007) no. 1, pp. 113-119. doi: 10.4064/am34-1-9

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