Finite Fresnel integrals
= Finite Fresnel integrals
{c}
{title2=$C(\lambda),S(\lambda)$}
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 $\pi t^2/2$.