# §13.5 Continued Fractions

If such that , and , then

where

13.5.2
,
.

This continued fraction converges to the meromorphic function of on the left-hand side everywhere in . For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).

If such that , and , then

where

13.5.4
,
.

This continued fraction converges to the meromorphic function of on the left-hand side throughout the sector .

See also Cuyt et al. (2008, pp. 322–330).