Computation of inhomogeneous Airy functions (Q1343651)

The inhomogeneous Airy functions: \[ Gi(x) = {1 \over \pi} \int^ \infty_ 0 \sin \left( xt + {1 \over 3} t^ 3 \right) dt, \quad Hi (x) = {1 \over \pi} \int^ \infty_ 0 \exp \left( xt - {1 \over 3} t^ 3 \right) dt \] are expanded into Chebyshev polynomial series with coefficients in precision of up to twenty decimal-places.