\begin{equation} \int_0^\infty \sin x^2 \, {\rm d}x = \frac{1}{2} \sqrt{\frac{\pi}{2}} \end{equation}
The most common proof goes with complex analysis. Try to provide a proof with Real Analysis.
Path
Welcome to mathimatikoi.org forum; Enjoy your visit here.
On the evaluation of the Fresnel integral
On the evaluation of the Fresnel integral
We are aware of the Fresnel integral
\begin{equation} \int_0^\infty \sin x^2 \, {\rm d}x = \frac{1}{2} \sqrt{\frac{\pi}{2}} \end{equation}
The most common proof goes with complex analysis. Try to provide a proof with Real Analysis.
\begin{equation} \int_0^\infty \sin x^2 \, {\rm d}x = \frac{1}{2} \sqrt{\frac{\pi}{2}} \end{equation}
The most common proof goes with complex analysis. Try to provide a proof with Real Analysis.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$