Created
June 2, 2017 13:56
-
-
Save hyuki0000/6658ef5d5f77adcbc40c7db53ad27566 to your computer and use it in GitHub Desktop.
第150回 波の広がり(後編) より https://cakes.mu/posts/12435
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
数列$\{a_n\}$と$\{b_n\}$を、 | |
$$ | |
\left\{ | |
\begin{align*} | |
a_0 &= \dfrac{1}{2\pi} \int_{0}^{2\pi} f(x) \,dx \\ | |
b_0 &= 0 \phantom{\int_{0}^{2\pi}}\\ | |
a_n &= \dfrac{1}{\pi} \int_{0}^{2\pi} f(x)\cos nx \,dx & (n = 1,2,3,\ldots)\\ | |
b_n &= \dfrac{1}{\pi} \int_{0}^{2\pi} f(x)\sin nx \,dx \\ | |
\end{align*} | |
\right. | |
$$ | |
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。 |
Author
hyuki0000
commented
Jun 2, 2017
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment