查看“︁Q梅西纳-帕拉泽克多项式”︁的源代码

[[File:QMEIXNER-POLLACZEK 2D PLOT.gif|thumb|QMEIXNER-POLLACZEK 2D PLOT]]
'''Q梅西纳-帕拉泽克多项式'''定义如下：<ref>Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analoques, p460,Springer</ref>

<math>P_{n}(x;a|q)=a^{-n}e^{in\phi}</math><math>\frac{a^2;q_n}{(q;q)_n}</math><math>_3\Phi_2(q^-n,ae^{i(\theta+2\phi)},ae^{-i\theta};a^2,0|q;q)</math>

==极限关系==
[[连续q哈恩多项式]]→'''Q梅西纳-帕拉泽克多项式'''

<math>\frac{p_{n}(cos(\theta+\phi);a,0,0,a;q)}{(q;q)_{n}}=P_{n}(cos(\theta+\phi);a|q)</math>

'''Q梅西纳-帕拉泽克多项式'''→[[连续q超球面多项式]]

<math>P_{n}(cos\phi;\beta|q)=C_{n}(cos\phi);\beta|q)</math>

'''Q梅西纳-帕拉泽克多项式'''→[[连续q拉盖尔多项式]]

<math>P_{n}(cos(\theta+\phi);q^{\alpha/2+1/2}|q)=</math><math>q^{(-\alpha/2-1/4)*n}*P_{n}^(\alpha)(cos\theta|q)</math>

==图集==
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|[[File:QMEIXNER-POLLACZEK IM COMPLEX 3D MAPLE PLOT.gif|thumb|QMEIXNER-POLLACZEK IM COMPLEX 3D MAPLE PLOT]]
|[[File:QMEIXNER-POLLACZEK RE COMPLEX 3D MAPLE PLOT.gif|thumb|QMEIXNER-POLLACZEK RE COMPLEX 3D MAPLE PLOT]]
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|[[File:QMEIXNER-POLLACZEK IM DENSITY MAPLE PLOT.gif|thumb|QMEIXNER-POLLACZEK IM DENSITY MAPLE PLOT]]
|[[File:QMEIXNER-POLLACZEK RE DENSITY MAPLE PLOT.gif|thumb|QMEIXNER-POLLACZEK RE DENSITY MAPLE PLOT]]
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==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-模拟]]
[[Category:Q超几何多项式]]
{{q超几何函数}}