查看“︁Q梅西纳多项式”︁的源代码

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'''Q梅西纳多项式'''以[[基本超几何函数]]定义如下：

<math>M_n(q^{-x};b,c;q)=_2\Phi_1(q^{-n},q^{-x};bq;q;-q^{n+1}/c)</math>
==极限关系==
;'''Q梅西纳多项式'''→[[Q拉盖尔多项式]];
令Q梅西纳多项式中<math>b=q^\alpha</math>,以及<math>q^{-x}=cq^{\alpha}x</math>,然后取<math>c  \to  \infty</math>即得Q拉盖尔多项式。

<math>\lim_{c \to \infty}M_{n}(cq^{\alpha}x;q^{\alpha},c;q)=\frac{(q;q)_{n}}{(q^{\alpha+1};q)_{n}}</math>
==图集==
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|[[File:QMEIXNER POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT.gif|thumb|QMEIXNER POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT]]
|[[File:QMEIXNER POLYNOMIALS IM COMPLEX 3D MAPLE PLOT.gif|thumb|QMEIXNER POLYNOMIALS IM COMPLEX 3D MAPLE PLOT]]
|[[File:QMEIXNER POLYNOMIALS RE COMPLEX 3D MAPLE PLOT.gif|thumb|QMEIXNER POLYNOMIALS RE COMPLEX 3D MAPLE PLOT]]
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|[[File:QMEIXNER POLYNOMIALS ABS DENSITY MAPLE PLOT.gif|thumb|QMEIXNER POLYNOMIALS ABS DENSITY MAPLE PLOT]]
|[[File:QMEIXNER POLYNOMIALS IM DENSITY MAPLE PLOT.gif|thumb|QMEIXNER POLYNOMIALS IM DENSITY MAPLE PLOT]]
|[[File:QMEIXNER POLYNOMIALS RE DENSITY MAPLE PLOT.gif|thumb|QMEIXNER POLYNOMIALS 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:基本超几何函数]]
{{q超几何函数}}
[[Category:Q超几何多项式]]