With arguments suppressed,
For , , and see (33.4.1).
The continued fraction (33.8.1) converges for all finite values of
, and (33.8.2) converges for all .
If we denote and
The ambiguous sign in (33.8.4) has to agree with that of the final
denominator in (33.8.1) when the continued fraction has converged
to the required precision. For proofs and further information see
Barnett et al. (1974) and Barnett (1996).