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]

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

$x=cos(\theta )$

极限关系

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

CONTINUOUS BIG Q-HERMITE POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT

CONTINUOUS BIG Q-HERMITE POLYNOMIALS IM COMPLEX 3D MAPLE PLOT

CONTINUOUS BIG Q-HERMITE POLYNOMIALS RE COMPLEX 3D MAPLE PLOT

CONTINUOUS BIG Q-HERMITE POLYNOMIALS ABS DENSITY MAPLE PLOT

CONTINUOUS BIG Q-HERMITE POLYNOMIALS IM DENSITY MAPLE PLOT

CONTINUOUS BIG Q-HERMITE POLYNOMIALS RE DENSITY MAPLE PLOT

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

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Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F., http://dlmf.nist.gov/18 |contribution-url=缺少标题 (帮助), Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248
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