Digital Library of Mathematical Functions
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33 Coulomb FunctionsVariables ρ,η

§33.4 Recurrence Relations and Derivatives

For =1,2,3,, let

33.4.1 R =1+η22,
S =ρ+η,
T =S+S+1.

Then, with X denoting any of F(η,ρ), G(η,ρ), or H±(η,ρ),

33.4.2 RX-1-TX+R+1X+1=0,
1,
33.4.3 X=RX-1-SX,
1,
33.4.4 X=S+1X-R+1X+1,
0.