# §25.2 Definition and Expansions

## §25.2(i) Definition

When ,

25.2.1

Elsewhere is defined by analytic continuation. It is a meromorphic function whose only singularity in is a simple pole at , with residue 1.

## §25.2(ii) Other Infinite Series

For further expansions of functions similar to (25.2.1) (Dirichlet series) see §27.4. This includes, for example, .

## §25.2(iv) Infinite Products

25.2.11,

product over all primes .

25.2.12

product over zeros of with (see §25.10(i)); is Euler’s constant (§5.2(ii)).