连续大Q埃尔米特多项式

连续大Q埃尔米特多项式是以基本超几何函数定义的正交多项式^[1]

${\displaystyle H_{n}(x;a;q)=a^{-n}\;_{2}\phi _{1}\left({\begin{matrix}q^{-n}&ae^{I\theta }&ae^{-I\theta }\\0&0\end{matrix}};q,q\right)}$

${\displaystyle x=cos(\theta )}$

令阿拉-萨拉姆-迟哈剌多项式 b=0,即得[[连续大Q埃尔米特多项式}}

令连续大Q埃尔米特多项式 a=0,即得连续埃尔米特多项式

1. ^ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p509,Springer,2010

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