查看“︁双Q克拉夫楚克多项式”︁的源代码

'''双Q克拉夫楚克多项式'''是一个以[[基本超几何函数]]定义的[[正交多项式]]<ref name=r>Roelof Koekoek, p505</ref>

<math>K_n(\lambda(x);c,N|q)=_3\Phi_2(q^{-n},q^{-x},cq^{x-N};q^{-N},0|q;q)</math>

==关系式==
*令[[Q拉卡多项式]]中<math>a=b</math>,<math>cq=q^{-N}</math> 即得'''双Q克拉夫楚克多项式'''
*令[[双q哈恩多项式]]中<math>d=c\gamma^{-1}q^{-N-1}</math>,且<math>\gamma</math>→0,即得'''双Q克拉夫楚克多项式'''
*令'''双Q克拉夫楚克多项式'''<math>c=1=p^{-1}</math>,并令q→1,即得[[克拉夫楚克多项式]]

==图集==
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|[[File:DUAL Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT.gif|thumb|DUAL Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT]]
|[[File:DUAL Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT.gif|thumb|DUAL Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT]]
|[[File:DUAL Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT.gif|thumb|DUAL Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT]]
|}
{|
|[[File:DUAL Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT.gif|thumb|DUAL Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT]]
|[[File:DUAL Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT.gif|thumb|DUAL Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT]]
|[[File:DUAL Q-KRAWTCHOUK POLYNOMIALS RE DENSITY MAPLE PLOT.gif|thumb|DUAL Q-KRAWTCHOUK POLYNOMIALS 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:基本超几何函数]]
{{q超几何函数}}