We indicate here how to obtain the limiting forms of
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).