Digital Library of Mathematical Functions
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33 Coulomb FunctionsVariables r,ϵ

§33.17 Recurrence Relations and Derivatives

33.17.1 (+1)rf(ϵ,-1;r)-(2+1)((+1)-r)f(ϵ,;r)+(1+(+1)2ϵ)rf(ϵ,+1;r)=0,
33.17.2 (+1)(1+2ϵ)rh(ϵ,-1;r)-(2+1)((+1)-r)h(ϵ,;r)+rh(ϵ,+1;r)=0,
33.17.3 (+1)rf(ϵ,;r) =((+1)2-r)f(ϵ,;r)-(1+(+1)2ϵ)rf(ϵ,+1;r),
33.17.4 (+1)rh(ϵ,;r) =((+1)2-r)h(ϵ,;r)-rh(ϵ,+1;r).