§33.25 Approximations

Keywords:: Coulomb functions: variables $\rho,\eta$ , Coulomb phase shift
Permalink:: http://dlmf.nist.gov/33.25

Cody and Hillstrom (1970) provides rational approximations of the phase shift $\mathop{{\sigma _{{0}}}\/}\nolimits\!\left(\eta\right)=\mathop{\mathrm{ph}\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(1+i\eta\right)$ (see (33.2.10)) for the ranges $0\leq\eta\leq 2$ , $2\leq\eta\leq 4$ , and $4\leq\eta\leq\infty$ . Maximum relative errors range from 1.09×10⁻²⁰ to 4.24×10⁻¹⁹.