查看“︁查理耶多项式”︁的源代码

[[File:Charlier polynomials 1.gif|thumb|Charlie polynomial]]
[[File:Charlier polynomials 2.gif|thumb|Charlie polynomial]]
'''查理耶多项式'''（Charlier polynomials)是一个以瑞典天文学家Carl Charlier命名的正交多项式，由下列[[拉盖尔多项式]]定义<ref>Szegő, Gabor (1939), Orthogonal Polynomials, Colloquium Publications – American Mathematical Society, ISBN 978-0-8218-1023-1, MR 0372517</ref>


:<math>\sum_{x=0}^\infty \frac{\mu^x}{x!} C_n(x; \mu)C_m(x; \mu)=\mu^{-n} e^\mu n! \delta_{nm}, \quad \mu>0.</math>


前几个查理耶多项式为

<math>\begin{align} 
  C0 & = 1  \\

  C1 & = x-1/mu  \\
  C2 & = -x+x^2+2/mu-2*x/mu+2/((2-2*x)*mu^2)-2*x/((2-2*x)*mu^2)  \\
  C3 & = 2*x-3*x^2+x^3-6/mu+9*x/mu-3*x^2/mu-12/((2-2*x)*mu^2)+18*x/((2-2*x)*mu^2)-6*x^2/((2-2*x)*mu^2)-12/((2-2*x)*(6-3*x)*mu^3)+18*x/((2-2*x)*(6-3*x)*mu^3)-6*x^2/((2-2*x)*(6-3*x)*mu^3) \\
\end{align}</math>

==参考文献==
<references/>

[[Category:正交多项式]]