Scorer's function

Summary

Scorer's functions $\operatorname{Gi}$ and $\operatorname{Hi}$ are particular solutions of the inhomogeneous Airy equations $y'' - x y = \mp\frac{1}{\pi}$. They are built from the same integrals as the Airy functions, split into two pieces. Their sum is the Airy function $\operatorname{Bi}$. They appear when a turning-point problem has a constant forcing term.