查看“︁双哈恩多项式”︁的源代码

[[File:Dual Hahn polynomials 1.gif|thumb|Dual Hahn polynomials plot]]
[[File:Dual Hahn polynomials 2.gif|thumb|Dual Hahn polynomials plot]]
'''双重哈恩多项式'''(Dual Hahn polynomials)是一个正交多项式，定义如下<ref>Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York</ref>

:<math>R_n(\lambda(x);\gamma,\delta,N)= {}_3F_2(-n,-x,x+\gamma+\delta+1;\gamma+1,-N;1).</math>  其中0≤''n''≤''N''

双重哈恩多项式的前几个：

==正交性==
双重哈恩多项式满足下列正交关系：<ref name=K>KoeKoef p209</ref>

<math>\sum_{x=0}^{N} \frac{(2x+\gamma+\delta+1)(\gamma+1)_{x}(-N)_{x}N!}{  (-1)^x(x+\gamma+\delta+1)_{N+1}(\delta+1)_{x}x!}</math>*
<math>R_{m}(\lambda(x);\gamma,\delta,N)R_{n}(\lambda(x);\gamma,\delta,N)=\frac{\delta_{mn}}{{\gamma+n \choose n}{\delta+N-n \choose  N-n}}</math>


==极限关系==
;[[拉卡多项式]]→[[双重哈恩多项式]]

<math>\lim_{\beta \to \infty}R_{n}(\lambda(x);-N-1,\beta,\gamma,\delta)=R_{n}(\lambda(\lim_{\beta \to \infty}R_{n}(\lambda(x);-x);\gamma,\delta,N)</math>
;[[双重哈恩多项式]]→[[梅西纳多项式]]

<math>\lim_{N \to \infty}R_{n}(\lambda(x);\beta-1,N(1-c)c^{-1},N)=M_{n}(x;\beta,c)</math>

==参考文献==
<references/>
{{q超几何函数}}
[[Category:正交多项式]]