Closed KoeTsukakoshi closed 1 year ago
\begin{align} \left( \int0^\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} = \frac{\pi}{2} \end{align}
\begin{align} \left( \int0^\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} = \frac{\pi}{2} \end{align}