# §33.8 Continued Fractions

With arguments suppressed,

For , , and see (33.4.1).

where

33.8.3

The continued fraction (33.8.1) converges for all finite values of , and (33.8.2) converges for all .

If we denote and , then

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).