The FunctionAdvisor(asymptotic_expansion, math_function) command returns the asymptotic expansion of the function, if possible.

$\mathrm{FunctionAdvisor}\left(\mathrm{asymptotic\_expansion}\,\arcsin \right)$

$\mathrm{asympt}\left(\arcsin \left(z\right)\,z\,4\right)=-\mathrm{I}\left(\ln \left(2\right)+\frac{\mathrm{I}\mathrm{\pi }}{2}+\ln \left(z\right)\right)+\frac{\mathrm{I}}{4z^2}+\mathrm{O}\left(\frac{1}{z^4}\right)$

$\mathrm{FunctionAdvisor}\left(\mathrm{asymptotic\_expansion}\,\mathrm{erf}\right)$

$\mathrm{asympt}\left(\mathrm{erf}\left(z\right)\,z\,4\right)=1+\frac{-\frac{1}{\sqrt{\mathrm{\pi }}z}+\frac{1}{2\sqrt{\mathrm{\pi }}{z}^3}+\mathrm{O}\left(\frac{1}{z^5}\right)}{{\ⅇ}^{z^2}}$

$\mathrm{FunctionAdvisor}\left(\mathrm{asymptotic\_expansion}\,\mathrm{FresnelS}\right)$

$\mathrm{asympt}\left(\mathrm{FresnelS}\left(z\right)\,z\,4\right)=\frac{1}{2}-\frac{\cos \left(\frac{\mathrm{\pi }{z}^2}{2}\right)}{\mathrm{\pi }z}-\frac{\sin \left(\frac{\mathrm{\pi }{z}^2}{2}\right)}{{\mathrm{\pi }}^2{z}^3}+\mathrm{O}\left(\frac{1}{z^5}\right)$

$\mathrm{has}\left(\,z\right)$

$\mathrm{false}$

$\mathrm{FunctionAdvisor}\left(\mathrm{asymptotic\_expansion}\,\mathrm{FresnelS}\left(z\right)\right)$

$\mathrm{asympt}\left(\mathrm{FresnelS}\left(z\right)\,z\,4\right)=\frac{1}{2}-\frac{\cos \left(\frac{\mathrm{\pi }{z}^2}{2}\right)}{\mathrm{\pi }z}-\frac{\sin \left(\frac{\mathrm{\pi }{z}^2}{2}\right)}{{\mathrm{\pi }}^2{z}^3}+\mathrm{O}\left(\frac{1}{z^5}\right)$

$\mathrm{has}\left(\,z\right)$

$\mathrm{true}$