<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">数列$\{a_n\}$と$\{b_n\}$を、
$$
\left\{
\begin{align*}
a_0 &amp;= \dfrac{1}{2\pi} \int_{0}^{2\pi} f(x) \,dx \\
b_0 &amp;= 0 \phantom{\int_{0}^{2\pi}}\\
a_n &amp;= \dfrac{1}{\pi} \int_{0}^{2\pi} f(x)\cos nx \,dx &amp; (n = 1,2,3,\ldots)\\
b_n &amp;= \dfrac{1}{\pi} \int_{0}^{2\pi} f(x)\sin nx \,dx \\
\end{align*}
\right.
$$
で定めると、
$$
f(x) = \sum_{k = 0}^{\infty} \left(a_k\cos kx + b_k\sin kx\right)
$$
が成り立つ。
</pre></body></html>