Q哈恩多项式

$Q_{n}(x;a,b,N;q)=\;_{3}\phi _{2}\left[{\begin{matrix}q^{-}n&abq^{n}+1&x\\aq&q^{-}N\end{matrix}};q,q\right]$

q哈恩多项式是哈恩多项式的q模拟，以基本超几何函数定义如下

极限关系

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

Q哈恩多项式→ 哈恩多项式

令 $\alpha =q^{\alpha }$ , $\beta =q^{\beta }$ 得

： Hypergeom([-n, alpha+beta+n+1, -x], [alpha+1, -N], 1)，即哈恩多项式

Q-HAHN ABS COMPLEX3D MAPLE PLOT

Q-HAHN IM COMPLEX3D MAPLE PLOT

Q-HAHN RE COMPLEX3D MAPLE PLOT

Q-HAHN ABS DENSITY MAPLE PLOT

Q-HAHN IM DENSITY MAPLE PLOT

Q-HAHN RE DENSITY MAPLE PLOT

Frank Oliver,NIST Handbook of Mathematical Functions, p470, Cambridge University Press, 2010

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