We indicate here how to obtain the limiting forms of f(ϵ,ℓ;r), h(ϵ,ℓ;r), s(ϵ,ℓ;r), and c(ϵ,ℓ;r) as r→±∞, with ϵ and ℓ fixed, in the following cases:
When r→±∞ with ϵ>0, Equations (33.16.4)–(33.16.7) are combined with (33.10.1).
When r→±∞ with ϵ<0, Equations (33.16.10)–(33.16.13) are combined with
Corresponding approximations for s(ϵ,ℓ;r) and c(ϵ,ℓ;r) as r→∞ can be obtained via (33.16.17), and as r→-∞ via (33.16.18).
When r→±∞ with ϵ=0, combine (33.20.1), (33.20.2) with §§10.7(ii), 10.30(ii).
For asymptotic expansions of f(ϵ,ℓ;r) and h(ϵ,ℓ;r) as r→±∞ with ϵ and ℓ fixed, see Curtis (1964a, §6).