Scorer's function

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

:$mathrm\{Gi\}(x)\; =\; frac\{1\}\{pi\}\; int\_0^infty\; sinleft(frac\{t^3\}\{3\}\; +\; xt\; ight),\; dt$:$mathrm\{Hi\}(x)\; =\; frac\{1\}\{pi\}\; int\_0^infty\; expleft(-frac\{t^3\}\{3\}\; +\; xt\; ight),\; dt$

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