CVBB ACM Team

这是本文档旧的修订版！

---

\begin{aligned} G(F(x))&=x
G(F(x))^k&=x^k
(G^k)'\big(F\big)\times F'&=kx^{k-1}
\sum\limits_{i=0}i{G^k}[i]F^{i-1}F'&=kx^{k-1}
\sum\limits_{i=0}i{G^k}[i]F^{i-n-1}F'&=kx^{k-1}F^{-n}
[x^{-1}]\sum\limits_{i=0}i{G^k}[i]F^{i-n-1}F'&=[x^{-1}]kx^{k-1}F^{-n}
\sum\limits_{i=0}i{G^k}[i]\big[i-n-1=-1\big]&=k[x^{-k}]F^{-n}
nG^k[n]&=k[x^{-k}]F^{-n}
\end{aligned} G(F(x)) G(F(x)) k

(G k ) ′ (F)×F ′

i=0 ∑ ​ iG k [i]F i−1 F ′

i=0 ∑ ​ iG k [i]F i−n−1 F ′

[x −1 ] i=0 ∑ ​ iG k [i]F i−n−1 F ′

i=0 ∑ ​ iG k [i][i−n−1=−1] nG k [n] ​

=x =x k

=kx k−1

=kx k−1

=kx k−1 F −n

=[x −1 ]kx k−1 F −n

=k[x −k ]F −n

=k[x −k ]F −n

​