where the function j is as in §10.47(ii),
a-1=0, a0=(2ℓ+1)!!Cℓ(η), and
The series (33.9.1) converges for all finite values of
η and ρ.
In this subsection the functions J, I, and K
are as in §§10.2(ii) and 10.25(ii).
Here b2ℓ=b2ℓ+2=0, b2ℓ+1=1, and
The series (33.9.3) and (33.9.4) converge for all
finite positive values of |η| and ρ.
Next, as η→+∞ with ρ (>0) fixed,
For other asymptotic expansions of Gℓ(η,ρ) see
Fröberg (1955, §8) and Humblet (1985).