Limit transitions will be derived between the five parameter family of Askey-Wilson polynomials, the four parameter family of big $q$-Jacobi polynomials and the three parameter family of little$q$-Jacobi polynomials in $n$ variables associated with root system $BC$.These limit transitions generalize the known hierarchy structure betweenthese families in the one variable case. Furthermore it will be provedthat these three families are $q$-analogues of the three parameterfamily of $BC$ type Jacobi polynomials in $n$ variables. The limittransitions will be derived by taking limits of $q$-difference operatorswhich have these polynomials as eigenfunctions.
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机译：极限转换将在与根系统相关联的$ n $变量中的Askey-Wilson多项式的五个参数族，大$ q $ -Jacobi多项式的四个参数族和Little $ q $ -Jacobi多项式的三个参数族之间在一个变量的情况下，这些限制过渡概括了这些族之间的已知层次结构。此外，将证明这三个族是$ n $变量中$ BC $型Jacobi多项式的三个参数族的$ q $模拟。 limittransition将通过将这些多项式作为本征函数的$ q $-差分运算符的限制进行导出。
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