カテゴリー: フーリエ級数

\[ F\left(x\right)=\sum_{k=1}^{\infty}\frac{4}{\pi\left(2k-1\right)}\sin\left(\left(2k-1\right)x\right) \]

\[ F\left(x\right)=\lim_{\epsilon\rightarrow0}\frac{f\left(x+\epsilon\right)+f\left(x-\epsilon\right)}{2} \]

\[ \sum_{k=-n}^{n}\left|C_{k}\right|^{2}\leq\frac{1}{2\pi}\int_{-\pi}^{\pi}\left|f\left(x\right)\right|^{2}dx \]

\[ f\left(x\right)=\frac{a_{0}}{2}+\sum_{n=1}^{\infty}\left(a_{n}\cos\left(nx\right)+b_{n}\sin\left(nx\right)\right) \]

\[ \sum_{n=-\infty}^{\infty}a_{n}\overline{b_{n}}=\frac{1}{2\pi}\int_{-\pi}^{\pi}A\left(x\right)\overline{B\left(x\right)}dx \]

\[ c_{-n}=\overline{c_{n}} \]

\[ c_{m}=\frac{1}{2\pi}\int_{-\pi}^{\pi}f\left(x\right)e^{-imx}dx \]

\[ \frac{1}{2\pi}\int_{-\pi}^{\pi}e^{imx}e^{inx}dx=\delta_{m,n} \]