Elsewhere ζ(s) is defined by analytic continuation. It is a
meromorphic function whose only singularity in ℂ is a simple pole at
s=1, with residue 1.
For further expansions of functions similar to (25.2.1) (Dirichlet series)
see §27.4. This includes, for example, 1/ζ(s).
For B2k see §24.2(i), and for B~n(x)
product over all primes p.
product over zeros ρ of ζ with ℜρ>0 (see
§25.10(i)); γ is Euler’s constant