Completed L-function (awaiting review)

If the L-function $L(s)$ satisfies the functional equation \[ \Lambda(s) := N^{s/2} \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) \cdot L(s) = \varepsilon \overline{\Lambda}(1-s), \] then $\Lambda(s)$ is called the completed L-function.

The completed L-function is the product of the L-function and its gamma factors.