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.

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