查看“︁双q哈恩多项式”︁的源代码


'''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]]

<math>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)</math>

<math>n=1,2,3\cdots N</math>


==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<math>\beta =0</math>以及<math>\alpha{q}=q^{-N}</math>,即得双q哈恩多项式：

<math>R_{n}(\mu(x);q^{-N-1},0,\gamma,\delta|q)=R_{n}(\mu(x);\gamma,\delta,N|q)</math>


;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<math>\gamma=p</math>以及<math>\delta=0</math>即得仿克拉夫楚克多项式。

==图集==
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|[[File:DUAL QHAHN ABS COMPLEX3D MAPLE PLOT.gif|thumb|DUAL QHAHN ABS COMPLEX3D MAPLE PLOT]]
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|[[File:DUAL QHAHN RE COMPLEX3D MAPLE PLOT.gif|thumb|DUAL QHAHN RE COMPLEX3D MAPLE PLOT]]
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|[[File:DUAL QHAHN ABS DENSITY MAPLE PLOT.gif|thumb|DUAL QHAHN ABS DENSITY MAPLE PLOT]]
|[[File:DUAL QHAHN IM DENSITY MAPLE PLOT.gif|thumb|DUAL QHAHN IM DENSITY MAPLE PLOT]]
|[[File:DUAL QHAHN RE DENSITY MAPLE PLOT.gif|thumb|DUAL QHAHN RE DENSITY MAPLE PLOT]]
|}


==参考文献==

*{{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=[[Cambridge University Press]] | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | doi=10.2277/0521833574 | mr=2128719 | year=2004 | volume=96}}
*{{Citation | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010}}
*{{dlmf|id=18|title=|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}

[[Category:正交多项式]]
[[Category:Q-analogs]]
[[Category:特殊超几何函数]]
{{q超几何函数}}