 Finite Fresnel integrals

In the unscaled convention, the finite Fresnel integrals are $C(\lambda )={\int }_0^{\lambda }\cos (t^2)dt$ and $S(\lambda )={\int }_0^{\lambda }\sin (t^2)dt$. Their Taylor series follow by termwise integration. At infinity both tend to $\sqrt{\pi /8}$, and their oscillatory tails have asymptotic expansions obtained by integration by parts. This convention differs from the convention with phase $\pi t^2/2$.