Misc results

Theorem 383.1(Multinomial expansion).

$$\begin{array}{r}(x_1+x_2+\cdots +x_m{)}^n=\sum _{\begin{array}{c}{k}_1+\cdots +k_m=n\\ \\ k_1,\dots ,k_m⩾0\end{array}}(\genfrac{}{}{0ex}{}{n}{k_1,k_2,\dots ,k_m})x_1^{k_1}{x}_2^{k_2}\dots x_m^{k_m}.\end{array}$$

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