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

Gasper, George; Rahman, Mizan, , Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F., , Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, 2010, ISBN 978-3-642-05013-8, MR 2656096, doi:10.1007/978-3-642-05014-5
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), , Cambridge University Press, 2010, ISBN 978-0521192255, MR 2723248
Stanton, Dennis, , Geometriae Dedicata, 1981, 10 (1): 403–425, ISSN 0046-5755, MR 0608153, doi:10.1007/BF01447435

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