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：

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

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

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

参考文献

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