The previous constraint was removed.
A clarification regarding the correct constraints for Lerch’s transcendent
has been added in the text immediately below.
If is not an integer then ; if is a positive integer
then ; if is a non-positive integer then can be any complex number.
For other values of , is defined by analytic
continuation. This is the notation used in Erdélyi et al. (1953a, p. 27).
Lerch (1887) used
.
The Hurwitz zeta function (§25.11) and the
polylogarithm (§25.12(ii)) are special
cases: