カテゴリー: 代数学

\[ a^{k}+b^{k}=\left(1-\delta_{0,k}\right)\sum_{j=0}^{\left\lfloor \frac{k}{2}\right\rfloor }\left(-1\right)^{j}\frac{k}{k-j}C\left(k-j,j\right)\left(a+b\right)^{k-2j}\left(ab\right)^{j}+2\delta_{0,k} \]

\[ \sum_{k=-n}^{n}e^{ikx}=\frac{\sin\left\{ \left(n+\frac{1}{2}\right)x\right\} }{\sin\frac{x}{2}} \]

\[ \frac{1}{x(x+a)^{n}}=\frac{1}{a^{n}x}-\sum_{k=1}^{n}\left(\frac{1}{a^{n-k+1}(x+1)^{k}}\right) \]