RSS2.0
優れもんじゃMathJax
。\[
\frac{\pi}{2} =
\left( \int_{0}^{\infty} \frac{\sin x}{\sqrt{x}} dx \right)^2 =
\sum_{k=0}^{\infty} \frac{(2k)!}{2^{2k}(k!)^2} \frac{1}{2k+1} =
\prod_{k=1}^{\infty} \frac{4k^2}{4k^2 - 1}.
\quad (\text{Wallis' product})
\]
\[
\zeta(2)=\frac{\pi^{2}}{6}.
\quad (\text{Riemann Zeta Function (2)})
\]
\[
\zeta(-1)=-\frac{1}{12}.
\quad (\text{Riemann Zeta Function (-1)})
\]
\[
\frac{1}{\pi} = 12 \sum_{k=0}^{\infty} \frac{(-1)^k(6k)!(13591409+545140134k)}{(3k)!(k!)^3640320^{3k+3/2}}.
\quad (\text{Chudnovsky Formula for Pi})
\]
\[
(3, 1, 4) \equiv (1, 5, 9) + (2, 6, 5) (mod 10).
\quad (\text{Strange formula: D. Terr (pers. comm.) noted the curious identity})
\]
これ等は LaTeX format で記述してある。
\[
\frac{\pi}{2} =
\left( \int_{0}^{\infty} \frac{\sin x}{\sqrt{x}} dx \right)^2 =
\sum_{k=0}^{\infty} \frac{(2k)!}{2^{2k}(k!)^2} \frac{1}{2k+1} =
\prod_{k=1}^{\infty} \frac{4k^2}{4k^2 - 1}.
\quad (\text{Wallis' product})
\]
\[
\zeta(2)=\frac{\pi^{2}}{6}.
\quad (\text{Riemann Zeta Function (2)})
\]
\[
\zeta(-1)=-\frac{1}{12}.
\quad (\text{Riemann Zeta Function (-1)})
\]
\[
\frac{1}{\pi} = 12 \sum_{k=0}^{\infty} \frac{(-1)^k(6k)!(13591409+545140134k)}{(3k)!(k!)^3640320^{3k+3/2}}.
\quad (\text{Chudnovsky Formula for Pi})
\]
\[
(3, 1, 4) \equiv (1, 5, 9) + (2, 6, 5) (mod 10).
\quad (\text{Strange formula: D. Terr (pers. comm.) noted the curious identity})
\]
special thanks: MathJaxの使い方
くろきげん\[
\frac{1}{c^2}\frac{\partial^2\varphi}{\partial{t^2}}-\Delta\varphi=4\pi\rho.
\]
\[
\frac{1}{c^2}\frac{\partial^2\mathfrak{a}}{\partial{t^2}}-\Delta\mathfrak{a}=4\pi i.
\]
\[
\frac{\partial\rho}{\partial t}+div\ i=0.
\]
\[
\mathfrak{E}=-grad\ \varphi - \frac{1}{c}\frac{\partial\mathfrak{a}}{\partial{t}}.
\]
\[
\mathfrak{H}=rot\ \mathfrak{a}.
\]
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