33 Coulomb Functions Computation 33.24 Tables 33.26 Software

§33.25 Approximations

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Keywords:: Coulomb functions: variables $\rho,\eta$ , Coulomb phase shift, phase shift (or phase)
Permalink:: http://dlmf.nist.gov/33.25
See also:: Annotations for Ch.33

Cody and Hillstrom (1970) provides rational approximations of the phase shift ${\sigma_{0}}\left(\eta\right)=\operatorname{ph}\Gamma\left(1+\mathrm{i}\eta\right)$ (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.

33.24 Tables 33.26 Software

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