_Fresnel integrals_ are a class of integrals which in $\mathbb{R}$ take the form of $\int dx \sin{(ax^2)}$ and $\int dx \cos{(ax^2)}$ # Complex Fresnel Integrals ## Gaussian look-alike $\int_{-\infty}^{\infty} dx\,e^{iax^2}=\sqrt{\frac{i\pi}{a}}=e^{i\frac{\pi}{4}}\sqrt{\frac{\pi}{a}}$ ^cde7ef --- # Proofs and Examples ## Proof of Gaussian look-alike #MathematicalFoundations/Analysis/Integrals