查看“︁拉卡多项式”︁的源代码

{{TA|G1=Math}}
[[File:Racah polynomials.gif|thumb|300px|拉卡多项式]]
'''拉卡多项式'''（Racah polynomials）是数学中以Guilio Racah命名的正交多项式，由下列[[广义超几何函数]]定义<ref>Askey, Richard; Wilson, James (1979), "A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols", SIAM Journal on Mathematical Analysis 10 (5): 1008–1016</ref>

:<math>p_n(x(x+\gamma+\delta+1)) = {}_4F_3\left[\begin{matrix} -n &n+\alpha+\beta+1&-x&x+\gamma+\delta+1\\
\alpha+1&\gamma+1&\beta+\delta+1\\ \end{matrix};1\right].</math>

拉卡多项式的前数条是


<math>\begin{align}
         hypergeom([-1, -x, 2 + a + b, x + c + d + 1], [a + 1, c + 1, b + d + 1], 1) \\
         hypergeom([-2, -x, 3 + a + b, x + c + d + 1], [a + 1, c + 1, b + d + 1], 1) \\
         hypergeom([-3, -x, 4 + a + b, x + c + d + 1], [a + 1, c + 1, b + d + 1], 1)\\
         hypergeom([-4, -x, 5 + a + b, x + c + d + 1], [a + 1, c + 1, b + d + 1], 1) \\
         hypergeom([-5, -x, 6 + a + b, x + c + d + 1], [a + 1, c + 1, b + d + 1], 1)\\
         hypergeom([-6, -x, 7 + a + b, x + c + d + 1], [a + 1, c + 1, b + d + 1], 1).
         

\end{align}</math>

==极限关系==
;拉卡多项式→[[哈恩多项式]]

<math>\lim_{\delta \to \infty}R_{n}(\lambda(x);-N-1,\delta)=Q_{n}(x;\alpha,\beta,N) 

                                          </math>

;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(x);\gamma,\delta,N)                                                         </math>

==参考文献==
<references/>

[[Category:正交多项式]]