查看“︁本德尔·邓恩多项式”︁的源代码


[[File:Bender-Dunne polynomials.gif|thumb|300px|本德尔-邓恩多项式]]
'''本德尔·邓恩多项式'''(Bender-Dunne polynomials)是一个[[正交多项式]]，定义如下：<ref>Bender, Carl M.; Dunne, Gerald V. (1988), "Polynomials and operator orderings", Journal of Mathematical Physics 29 (8): 1727–1731, doi:10.1063/1.527869, ISSN 0022-2488, MR 955168</ref>.

<math>P_0(x) = 1</math>, 
: <math>P_{1}(x) = x</math> , 

当 <math>n > 1</math>:

: <math>P_n(x) = x P_{n-1}(x) + 16 (n-1) (n-J-1) (n + 2 s -2) P_{n-2}(x)</math>

==例子==
<math>\begin{align}
 P[2] &=x^2+32*s-32*s*J       \\
 P[3]&= x^3+160*x*s-96*x*s*J+64*x-32*x*J  \\
 P[4] &= x^4+448*x^2*s-192*x^2*s*J+352*x^2-128*x^2*J+9216*s-12288*s*J+9216*s^2-12288*s^2*J+3072*s*J^2+3072*s^2*J^2  .





\end{align}</math>





==参考文献==
<references/>

[[Category:正交多项式]]