Difference between revisions of "Fresnel S"
From specialfunctionswiki
| Line 16: | Line 16: | ||
</div> | </div> | ||
</div> | </div> | ||
| + | |||
| + | {{:*-integral functions footer}} | ||
Revision as of 06:53, 5 April 2015
The Fresnel $S$ function is defined by $$S(x)=\int_0^x \sin(t^2) dt.$$
- Fresnel.png
Fresnel integrals on $\mathbb{R}$.
Properties
Theorem: The following limit is known: $$\displaystyle\lim_{x \rightarrow \infty} S(x) = \displaystyle\int_0^{\infty} \sin(t^2)dt = \sqrt{ \dfrac{\pi}{8}}.$$
Proof: █
