双q哈恩多项式

双q哈恩多项式是一个以基本超几何函数定义的正交多项式

${\displaystyle R_{n}(\mu (x);\delta ,\gamma ,N|q)=_{3}\Phi _{2}(q^{-n},q^{-x},\gamma \delta {q}^{x+1};\gamma {q},q_{N};q,q)}$

${\displaystyle n=1,2,3\cdots N}$

极限关系

Q拉卡多项式→双q哈恩多项式；

在Q拉卡多项式中令${\displaystyle \beta =0}$以及${\displaystyle \alpha {q}=q^{-N}}$,即得双q哈恩多项式：

${\displaystyle R_{n}(\mu (x);q^{-N-1},0,\gamma ,\delta |q)=R_{n}(\mu (x);\gamma ,\delta ,N|q)}$

双q哈恩多项式→仿射克拉夫楚克多项式

在双q哈恩多项式中令${\displaystyle \gamma =p}$以及${\displaystyle \delta =0}$即得仿克拉夫楚克多项式。

图集

DUAL QHAHN ABS COMPLEX3D MAPLE PLOT

DUAL QHAHN IM COMPLEX3D MAPLE PLOT

DUAL QHAHN RE COMPLEX3D MAPLE PLOT

DUAL QHAHN ABS DENSITY MAPLE PLOT

DUAL QHAHN IM DENSITY MAPLE PLOT

DUAL QHAHN RE DENSITY MAPLE PLOT

参考文献

• Gasper, George; Rahman, Mizan, Basic hypergeometric series, 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., Hypergeometric orthogonal polynomials and their q-analogues, 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), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248