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Mathematica 教學：級數係數

由 戴忠淵 於 2014年8月12日星期二 下午2:29 發表 





Unprotect[Power];0^0:=1;Protect[Power];
f=(p0*z)^k(1-p0*z)(1-p0*z-q0*z*(1-(p0*z)^k))^(-1);
D[f,{z,1}]/.k->1/.z->0
D[f,{z,2}]/2/.k->1/.z->0//Simplify
D[f,{z,3}]/6/.k->1/.z->0//Simplify
D[f,{z,4}]/24/.k->1/.z->0//Simplify
test1=Table[(D[f,{z,n}]/n!/.k->1/.z->0),{n,1,10}]//Simplify
SeriesCoefficient[f/.k->1,{z,0,n}]
test2=SeriesCoefficient[f/.k->1,{z,0,#}]&/@Range[10]//Simplify
test1===test2

mytable[{kl_,ku_},{nl_,nu_}]:=
TableForm[Table[SeriesCoefficient[f/.k->kk,{z,0,nn}],
{kk,kl,ku},{nn,nl,nu}],
TableHeadings->{Range[kl,ku],"第"<>ToString[#]<>"項"&/@Range[nl,nu]}]

mytable[{11,20},{8,15}]
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