= Fresnel tail expansion
{c}
{title2=$C=A+P\sin\lambda^2-Q\cos\lambda^2$}
For $A=\sqrt{\pi/8}$, define real tail functions by $Q+iP=e^{-i\lambda^2}\int_\lambda^\infty e^{it^2}dt$. Then $C=A+P\sin\lambda^2-Q\cos\lambda^2$ and $S=A-P\cos\lambda^2-Q\sin\lambda^2$. Repeated <integration by parts> gives
$$
P\sim\sum_{m\ge0}\frac{(-1)^m(4m-1)!!}{2^{2m+1}\lambda^{4m+1}},\qquad Q\sim\sum_{m\ge0}\frac{(-1)^m(4m+1)!!}{2^{2m+2}\lambda^{4m+3}},
$$
where $(-1)!!=1$. These are <asymptotic expansions>, rather than convergent infinite sums at a fixed argument.
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