查看“︁Q哈恩多项式”︁的源代码

'''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

<math>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] </math>
==极限关系==
'''Q哈恩多项式'''→    [[量子Q克拉夫楚克多项式]]：

<math>\lim_{a \to \infty}Q_{n}(q^-{x};a;p,N|q)=K_{n}^{qtm}(q^-{x};p,N;q)</math>

'''Q哈恩多项式'''→  [[哈恩多项式]]

令<math>\alpha=q^{\alpha}</math>,<math>\beta=q^{\beta}</math> 得

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

==图集==
{|
|[[File:Q-HAHN ABS COMPLEX3D MAPLE PLOT.gif|thumb|Q-HAHN ABS COMPLEX3D MAPLE PLOT]]
|[[File:Q-HAHN IM COMPLEX3D MAPLE PLOT.gif|thumb|Q-HAHN IM COMPLEX3D MAPLE PLOT]]
|[[File:Q-HAHN RE COMPLEX3D MAPLE PLOT.gif|thumb|Q-HAHN RE COMPLEX3D MAPLE PLOT]]
|}
{|
|[[File:Q-HAHN ABS DENSITY MAPLE PLOT.gif|thumb|Q-HAHN ABS DENSITY MAPLE PLOT]]
|[[File:Q-HAHN IM DENSITY MAPLE PLOT.gif|thumb|Q-HAHN IM DENSITY MAPLE PLOT]]
|[[File:Q-HAHN RE DENSITY MAPLE PLOT.gif|thumb|Q-HAHN RE DENSITY MAPLE PLOT]]
|}

==参考文献==
<references/>
Frank Oliver,NIST Handbook of Mathematical Functions, p470, Cambridge University Press, 2010


[[Category:正交多项式]]
{{q超几何函数}}
[[Category:Q超几何多项式]]