Elsewhere is defined by analytic continuation. It is a
meromorphic function whose only singularity in is a simple pole at
, with residue 1.
For further expansions of functions similar to (25.2.1) (Dirichlet series)
see §27.4. This includes, for example, .
For see §24.2(i), and for
product over all primes .
product over zeros of with (see
§25.10(i)); is Euler’s constant