Fibonacci多项式的组合性质

<title>Combination of Fibobnacci Polynomial

利用经典的分析知识来研究Fibonacci多项式的组合性质:∑a1+a2+…+ak=nFa1+1(x) Fa2+1(x)…Fak+1(x)=∑[n+k2-1]l=0Cln+k-l-1Ck-1n+k-2l-1xn-2l,并得到一个有趣的结果:∑a1+a2+…+ak=nFa1+1 Fa2+1…Fak+1=∑[n+k2-1]l=0Cln+k-l-1Ck-1n+k-2l-1.

<Abstrcat>The typical analytical mathematical knowledge is applied in the research of the combination property of Fibobnacci polynomial∑a1+a2+...+ak=nFa1+1(x)Fa2+1(x)...Fak+1(x)=∑糞X(〗n+k2-1]l=0Cln+k-l-1Ck-1n+k-2l-1xn-2l,And an interesting result is obtained:∑a1+a2+...+ak=nFa1·Fa2...Fak+1=∑糞X(〗n+k2-1]l=0Cln+k-l-1Ck-1n+k-2l-1