Coulomb Wave Functions in the Transition Region

Expansions, involving the Airy integrals, of the functions $F_L(\eta , \rho )$, $G_L(\eta , \rho )$ are obtained from a study of the Coulomb wave equation. These expansions are convergent in the region $|\rho -{\rho }_1|<\mathrm{}{\rho }_1$, where ${\rho }_1=\eta +{[{\eta }^2+L(L+1\mathrm{}\left)\right]}^{\frac{1}{2}}.$