梅西纳多项式

Meixner polynomials 3D animation

Meixner polynomials 3D animation

Meixner polynomials 3D animation

梅西纳多项式定义为

$M_n(x,\beta ,\gamma )=\sum _{k=0}^n(-1{)}^k(\genfrac{}{}{0ex}{}{n}{k})(\genfrac{}{}{0ex}{}{x}{k})k!(x-\beta {)}_{n-k}{\gamma }^{-k}$

梅西纳多项式的前几项为：

$Mx[1]:=[-\beta -(1-\gamma )*x/\gamma ]$

$Mx[2]:=[({\gamma }^2*{\beta }^2-\beta *{\gamma }^2)/{\gamma }^2+({\gamma }^2-2*\beta *{\gamma }^2-1+2*\gamma *\beta )*x/{\gamma }^2+(-2*\gamma +1+{\gamma }^2)*x^2/{\gamma }^2]$

$Mx[3]:=[-({\gamma }^3*{\beta }^3-3*{\gamma }^3*{\beta }^2+2*{\gamma }^3*\beta )/{\gamma }^3-(-3*{\gamma }^3*{\beta }^2+3*{\gamma }^2*{\beta }^2-3*\gamma *\beta +6*{\gamma }^3*\beta -2*{\gamma }^3-3*\beta *{\gamma }^2+2)*x/{\gamma }^3-(-3*{\gamma }^3+3*{\gamma }^3*\beta +3*{\gamma }^2-6*\beta *{\gamma }^2+3*\gamma *\beta -3+3*\gamma )*x^2/{\gamma }^3-(3*{\gamma }^2-3*\gamma -{\gamma }^3+1)*x^3/{\gamma }^3]$

参考文献

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