查看“︁量子Q克拉夫楚克多项式”︁的源代码


'''量子Q克拉夫楚克多项式'''是以[[基本超几何函数]]定义的[[正交多项式]]<ref>Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p493,Springer,2010</ref>




<math>K^{qtm}_{n}(q^{-x};p;N;q)=\;_{2}\phi_1\left(\begin{matrix} 
q^{-n} & q^{-x}   \\ 
q^{-N}   \end{matrix} 
; q,pq^{n+1} \right)</math>

<math>n=0,1,2,\cdots N</math>

==极限关系==
[[Q哈恩多项式]]→    量子Q克拉夫楚克多项式：

<math>\lim_{a \to \infty}Q_{n}(q^-{x};a;p,N|q)=K_{n}^{qtm}(q^-{x};p,N;q)</math>

量子Q克拉夫楚克多项式→ [[克拉夫楚克多项式]]：

<math>\lim_{a \to 1}=K_{n}^{qtm}(q^-{x};p,N;q)=K_{n}(x;p^{-1},N)</math>

==图集==
{|
|[[File:QUANTUM Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT.gif|thumb|QUANTUM Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT]]
|[[File:QUANTUM Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT.gif|thumb|QUANTUM Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT]]
|[[File:QUANTUM Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT.gif|thumb|QUANTUM Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT]]
|}
{|
|[[File:QUANTUM Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT.gif|thumb|QUANTUM Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT]]
|[[File:QUANTUM Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT.gif|thumb|QUANTUM Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT]]
|[[File:QUANTUM Q-KRAWTCHOUK POLYNOMIALS RE DENSITY MAPLE PLOT.gif|thumb|QUANTUM Q-KRAWTCHOUK POLYNOMIALS RE DENSITY MAPLE PLOT]]
|}


==参考文献==
<references/>
*{{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}}
*{{Citation | last1=Stanton | first1=Dennis | title=Three addition theorems for some q-Krawtchouk polynomials | doi=10.1007/BF01447435 | mr=608153 | year=1981 | journal=Geometriae Dedicata | issn=0046-5755 | volume=10 | issue=1 | pages=403–425}}

[[Category:正交多项式]]
[[Category:基本超几何函数]]
{{q超几何函数}}