Generalized Jacobi polynomials and Selberg integrals
The authors employ \textit{G. W. Anderson}'s method [Forum Math. 3, No. 4, 415-417 (1991; Zbl 0723.33002)] for evaluating the Selberg integral \[ {1\over n!}\int_{[0,1]^n} \prod_{i=1}^n x_i^{a-1}(1-x_i)^{b-1}\prod_{1 \leq i < j \leq n} |x_i-x_j|^{2c} d{\mathbf x}, \] to obtain \textit{J. Kaneko}'s evaluation [Ann. Sci. Ec. Norm. Supér., IV. Sér. 29, No. 5, 583-637 (1996)] of \[ {1 \over n!}\int_{[0,1]^n} \prod_{j=1}^m \prod_{i=1}^n(y_j-x_i)^u \prod_{i=1}^n x_i^{a-1}(1-x_i)^{b-1}\prod_{1 \leq i < j \leq n} |x_i-x_j|^{2c} d{\mathbf x}. \]
scientific article; zbMATH DE number 907640