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where ''Z''(''s'') is ζ(''s'') multiplied by a ''gamma-factor'', involving the [[gamma function]]. This is now read as an 'extra' factor in the [[Euler product]] for the zeta-function, corresponding to the [[infinite prime]]. Just the same shape of functional equation holds for the [[Dedekind zeta function]] of a [[number field]] ''K'', with an appropriate gamma-factor that depends only on the embeddings of ''K'' (in algebraic terms, on the [[tensor product of fields|tensor product]] of ''K'' with the [[real number|real field]]).
There is a similar equation for the [[Dirichlet L-function]]s, but this time relating them in pairs:<Ref>{{cite web|url=https://dlmf.nist.gov/25.15 |title=§25.15 Dirichlet -functions on NIST}}</ref>
:<math>\Lambda(s,\chi)=\varepsilon\Lambda(1-s,\chi^*)</math>
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