In (8.6.10)–(8.6.12), is a real constant and the
path of integration is indented (if necessary) so that it separates the poles
of the gamma function from the other pole in the integrand, in the case of
(8.6.10) and (8.6.11), and from the poles at
in the case of (8.6.12).
For collections of integral representations of and
see Erdélyi et al. (1953b, §9.3),
Oberhettinger (1972, pp. 68–69),
Oberhettinger and Badii (1973, pp. 309–312),
Prudnikov et al. (1992b, §3.10), and
Temme (1996b, pp. 282–283).