Abstract
Elementary spherical functions on symmetric spaces can be considered as orthogonal polynomials in several variables. This paper deals with the weight function \[ w\left( {x_1 , \cdots ,x_l } \right) = \Pi \left( {1 - x_i } \right)^\alpha \left( {1 + x_i } \right)^\beta \Pi \left( {x_i - x_j } \right)^{2\gamma + 1} ,\quad - 1 \leq x_i \leq 1.\] Recurrence relations for polynomials corresponding to different spaces are derived and generalized to other values of the parameters $\alpha $, $\beta $ and $\gamma $.
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