Scorer's function

In mathematics, the Scorer's functions are special functions denoted Gi(x) and Hi(x). They can be defined as:

$\mathrm {Gi} (x)={\frac {1}{\pi }}\int _{0}^{\infty }\sin \left({\frac {t^{3}}{3}}+xt\right)\,dt$

$\mathrm {Hi} (x)={\frac {1}{\pi }}\int _{0}^{\infty }\exp \left(-{\frac {t^{3}}{3}}+xt\right)\,dt$

The Scorer's functions can also be defined in terms of Airy functions.