仿射q克拉夫楚克多項式

仿射q克拉夫楚克多項式是以基本超幾何函數定義的正交多項式^[1]

${\displaystyle K_{n}^{aff}(q^{-x};p;N;q)=\;_{2}\phi _{1}\left({\begin{matrix}q^{-n}&0&q^{-x}\\pq&q^{-N}\end{matrix}};q,q\right)}$

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

極限關係

Q哈恩多項式→ 量子Q克拉夫楚克多項式：

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

仿射q克拉夫楚克多項式→ 小q拉蓋爾多項式：

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

圖集

AFFINE Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT

AFFINE Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT

AFFINE Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT

AFFINE Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT

AFFINE Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT

AFFINE Q-KRAWTCHOUK POLYNOMIALS RE DENSITY MAPLE PLOT