Digital Library of Mathematical Functions
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33 Coulomb FunctionsVariables ρ,η

§33.3 Graphics

Contents

§33.3(i) Line Graphs of the Coulomb Radial Functions F(η,ρ) and G(η,ρ)

See accompanying text
Figure 33.3.1: F(η,ρ), G(η,ρ) with =0, η=-2. Magnify
See accompanying text
Figure 33.3.2: F(η,ρ), G(η,ρ) with =0, η=0. Magnify
See accompanying text
Figure 33.3.3: F(η,ρ), G(η,ρ) with =0, η=2. The turning point is at ρtp(2,0)=4. Magnify
See accompanying text
Figure 33.3.4: F(η,ρ), G(η,ρ) with =0, η=10. The turning point is at ρtp(10,0)=20. Magnify

In Figures 33.3.5 and 33.3.6

33.3.1 M(η,ρ)=(F2(η,ρ)+G2(η,ρ))1/2=|H±(η,ρ)|.
See accompanying text
Figure 33.3.5: F(η,ρ), G(η,ρ), and M(η,ρ) with =0, η=15/2. The turning point is at ρtp(15/2,0)=30=5.47. Magnify
See accompanying text
Figure 33.3.6: F(η,ρ), G(η,ρ), and M(η,ρ) with =5, η=0. The turning point is at ρtp(0,5)=30 (as in Figure 33.3.5). Magnify

§33.3(ii) Surfaces of the Coulomb Radial Functions F0(η,ρ) and G0(η,ρ)

Figure 33.3.7: F0(η,ρ), -2η2, 0ρ5. Magnify
Figure 33.3.8: G0(η,ρ), -2η2, 0<ρ5. Magnify