Wikipedia's article for the Selberg class tell us that the Riemann's Zeta function belongs to the class, thus satisfies the Definition.
I would like to know the details using this terminology of the axiom $3$ taking as specialization our Riemann's Zeta function $\zeta(s)$. Note also that seems that such axiom presumes the unicity of such representation (and of course I am agree with the axiom , but if you can clarify the meaning of this axiom with respect the unicity feel free to add it, if make sense this discussion).
Question. Can you prove rigurously that using the terminology explained in previous Wikipedia's article, the Riemann's Zeta function satisfies that has a functional equation? That is, can you evidence rigurously that the Riemann's Zeta function satisfies a functional equation in the spirit of the Selberg class? If you prefer provide us only hints to get such comparison between the functional equation and this description in the language of the Selberg class, free feel to do it as an answer. Thanks in advance.