\begin{split} & \lim_{R\rightarrow \infty} \ \lim_{a \rightarrow 0} \ \Phi(a)\sum_{\Lambda(a)\cap D(R)} \Big  \langle \phi \Big\vert \ \frac{0}{z-\zeta_{m,n}(a)} \Big\vert   \psi \Big \rangle  =\\ \\ &  \lim_{R\rightarrow \infty} \ \lim_{a \rightarrow 0} \ \int _{\mathbb{C}} d^{0}z \ \Phi(a)\sum_{\Lambda(a)\cap D(R)} \frac{\phi^{*}(z)\psi(z)}{z-\zeta_{m,n}(a)}