量子Q克拉夫楚克多项式

量子Q克拉夫楚克多项式是以基本超几何函数定义的正交多项式^[1]

${\displaystyle K_{n}^{qtm}(q^{-x};p;N;q)=\;_{2}\phi _{1}\left({\begin{matrix}q^{-n}&q^{-x}\\q^{-N}\end{matrix}};q,pq^{n+1}\right)}$

${\displaystyle n=0,1,2,\cdots N}$

Q哈恩多项式→ 量子Q克拉夫楚克多项式：

${\displaystyle \lim _{a\to \infty }Q_{n}(q^{-}{x};a;p,N|q)=K_{n}^{qtm}(q^{-}{x};p,N;q)}$

量子Q克拉夫楚克多项式→ 克拉夫楚克多项式：

${\displaystyle \lim _{a\to 1}=K_{n}^{qtm}(q^{-}{x};p,N;q)=K_{n}(x;p^{-1},N)}$

1. ^ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p493,Springer,2010

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