About the Project
33 Coulomb FunctionsVariables ρ,η

Β§33.4 Recurrence Relations and Derivatives

For β„“=1,2,3,…, let

33.4.1 Rβ„“ =1+Ξ·2β„“2,
Sβ„“ =ℓρ+Ξ·β„“,
Tβ„“ =Sβ„“+Sβ„“+1.

Then, with Xβ„“ denoting any of Fℓ⁑(Ξ·,ρ), Gℓ⁑(Ξ·,ρ), or Hℓ±⁑(Ξ·,ρ),

33.4.2 Rℓ⁒Xβ„“βˆ’1βˆ’Tℓ⁒Xβ„“+Rβ„“+1⁒Xβ„“+1=0,
β„“β‰₯1,
33.4.3 Xβ„“β€²=Rℓ⁒Xβ„“βˆ’1βˆ’Sℓ⁒Xβ„“,
β„“β‰₯1,
33.4.4 Xβ„“β€²=Sβ„“+1⁒Xβ„“βˆ’Rβ„“+1⁒Xβ„“+1,
β„“β‰₯0.