梅西納多項式

梅西納多項式定義為

Meixner polynomials 3D animation

Meixner polynomials 3D animation

Meixner polynomials 3D animation

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

梅西納多項式的前幾項為：

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

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

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

參考文獻

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