Throughout §§8.17 and 8.18 we assume that , , and . However, in the case of §8.17 it is straightforward to continue most results analytically to other real values of , , and , and also to complex values.
where, as in §5.12, denotes the Beta function:
Addendum: For a companion equation see (8.17.24).
For a historical profile of see Dutka (1981).
For the hypergeometric function see §15.2(i).
With , , and ,
where and the branches of and are continuous on the path and assume their principal values when .
The and convergents are less than , and the and convergents are greater than .
See also Cuyt et al. (2008, pp. 385–389).
For sums of infinite series whose terms involve the incomplete Beta function see Hansen (1975, §62).